22.6: Difference between revisions

Latest revision as of 11:57, 28 June 2021

DLMF	Formula	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
22.6.E1	${\displaystyle{\displaystyle{\operatorname{sn}^{2}}\left(z,k\right)+{% \operatorname{cn}^{2}}\left(z,k\right)=k^{2}{\operatorname{sn}^{2}}\left(z,k% \right)+{\operatorname{dn}^{2}}\left(z,k\right)}}$ `\Jacobiellsnk^{2}@{z}{k}+\Jacobiellcnk^{2}@{z}{k} = k^{2}\Jacobiellsnk^{2}@{z}{k}+\Jacobielldnk^{2}@{z}{k}`	(JacobiSN(z, k))^(2)+ (JacobiCN(z, k))^(2) = (k)^(2)* (JacobiSN(z, k))^(2)+ (JacobiDN(z, k))^(2)	(JacobiSN[z, (k)^2])^(2)+ (JacobiCN[z, (k)^2])^(2) == (k)^(2)* (JacobiSN[z, (k)^2])^(2)+ (JacobiDN[z, (k)^2])^(2)	Successful	Successful	-	Successful [Tested: 21]
22.6.E1	${\displaystyle{\displaystyle k^{2}{\operatorname{sn}^{2}}\left(z,k\right)+{% \operatorname{dn}^{2}}\left(z,k\right)=1}}$ `k^{2}\Jacobiellsnk^{2}@{z}{k}+\Jacobielldnk^{2}@{z}{k} = 1`	(k)^(2)* (JacobiSN(z, k))^(2)+ (JacobiDN(z, k))^(2) = 1	(k)^(2)* (JacobiSN[z, (k)^2])^(2)+ (JacobiDN[z, (k)^2])^(2) == 1	Successful	Successful	-	Successful [Tested: 21]
22.6.E2	${\displaystyle{\displaystyle 1+{\operatorname{cs}^{2}}\left(z,k\right)=k^{2}+{% \operatorname{ds}^{2}}\left(z,k\right)}}$ `1+\Jacobiellcsk^{2}@{z}{k} = k^{2}+\Jacobielldsk^{2}@{z}{k}`	1 + (JacobiCS(z, k))^(2) = (k)^(2)+ (JacobiDS(z, k))^(2)	1 + (JacobiCS[z, (k)^2])^(2) == (k)^(2)+ (JacobiDS[z, (k)^2])^(2)	Successful	Successful	-	Successful [Tested: 21]
22.6.E2	${\displaystyle{\displaystyle k^{2}+{\operatorname{ds}^{2}}\left(z,k\right)={% \operatorname{ns}^{2}}\left(z,k\right)}}$ `k^{2}+\Jacobielldsk^{2}@{z}{k} = \Jacobiellnsk^{2}@{z}{k}`	(k)^(2)+ (JacobiDS(z, k))^(2) = (JacobiNS(z, k))^(2)	(k)^(2)+ (JacobiDS[z, (k)^2])^(2) == (JacobiNS[z, (k)^2])^(2)	Successful	Successful	-	Successful [Tested: 21]
22.6.E3	${\displaystyle{\displaystyle{k^{\prime}}^{2}{\operatorname{sc}^{2}}\left(z,k% \right)+1={\operatorname{dc}^{2}}\left(z,k\right)}}$ `{k^{\prime}}^{2}\Jacobiellsck^{2}@{z}{k}+1 = \Jacobielldck^{2}@{z}{k}`	1 - (k)^(2)*(JacobiSC(z, k))^(2)+ 1 = (JacobiDC(z, k))^(2)	1 - (k)^(2)*(JacobiSC[z, (k)^2])^(2)+ 1 == (JacobiDC[z, (k)^2])^(2)	Failure	Failure	Failed [21 / 21] Result: .7126235439-1.151829144I Test Values: {z = 1/23^(1/2)+1/2I, k = 1} Result: .144618294+.733840068e-1I Test Values: {z = 1/23^(1/2)+1/2I, k = 2} ... skip entries to safe data	Failed [21 / 21] Result: Complex[0.7126235442208428, -1.1518291435850532] Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[0.14461829395996295, 0.07338400615035004] Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
22.6.E3	${\displaystyle{\displaystyle{\operatorname{dc}^{2}}\left(z,k\right)={k^{\prime% }}^{2}{\operatorname{nc}^{2}}\left(z,k\right)+k^{2}}}$ `\Jacobielldck^{2}@{z}{k} = {k^{\prime}}^{2}\Jacobiellnck^{2}@{z}{k}+k^{2}`	(JacobiDC(z, k))^(2) = 1 - (k)^(2)*(JacobiNC(z, k))^(2)+ (k)^(2)	(JacobiDC[z, (k)^2])^(2) == 1 - (k)^(2)*(JacobiNC[z, (k)^2])^(2)+ (k)^(2)	Failure	Failure	Failed [21 / 21] Result: .287376456+1.151829144I Test Values: {z = 1/23^(1/2)+1/2I, k = 1} Result: .855381706-.733840068e-1I Test Values: {z = 1/23^(1/2)+1/2I, k = 2} ... skip entries to safe data	Failed [21 / 21] Result: 1.0 Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[1.4338548818798933, 0.22015201845104385] Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
22.6.E4	${\displaystyle{\displaystyle-k^{2}{k^{\prime}}^{2}{\operatorname{sd}^{2}}\left% (z,k\right)=k^{2}({\operatorname{cd}^{2}}\left(z,k\right)-1)}}$ `-k^{2}{k^{\prime}}^{2}\Jacobiellsdk^{2}@{z}{k} = k^{2}(\Jacobiellcdk^{2}@{z}{k}-1)`	- (k)^(2)1 - (k)^(2)(JacobiSD(z, k))^(2) = (k)^(2)*((JacobiCD(z, k))^(2)- 1)	- (k)^(2)1 - (k)^(2)(JacobiSD[z, (k)^2])^(2) == (k)^(2)*((JacobiCD[z, (k)^2])^(2)- 1)	Failure	Failure	Failed [21 / 21] Result: -1.287376456-1.151829144I Test Values: {z = 1/23^(1/2)+1/2I, k = 1} Result: 4.672736560+.4694177821I Test Values: {z = 1/23^(1/2)+1/2I, k = 2} ... skip entries to safe data	Failed [21 / 21] Result: Complex[-1.2873764557791572, -1.1518291435850532] Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[4.672736560761239, 0.46941777772332965] Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
22.6.E4	${\displaystyle{\displaystyle k^{2}({\operatorname{cd}^{2}}\left(z,k\right)-1)=% {k^{\prime}}^{2}(1-{\operatorname{nd}^{2}}\left(z,k\right))}}$ `k^{2}(\Jacobiellcdk^{2}@{z}{k}-1) = {k^{\prime}}^{2}(1-\Jacobiellndk^{2}@{z}{k})`	(k)^(2)((JacobiCD(z, k))^(2)- 1) = 1 - (k)^(2)(1 - (JacobiND(z, k))^(2))	(k)^(2)((JacobiCD[z, (k)^2])^(2)- 1) == 1 - (k)^(2)(1 - (JacobiND[z, (k)^2])^(2))	Failure	Failure	Failed [21 / 21] Result: -1.287376456-1.151829144I Test Values: {z = 1/23^(1/2)+1/2I, k = 1} Result: 1.168184140+.1173544454I Test Values: {z = 1/23^(1/2)+1/2I, k = 2} ... skip entries to safe data	Failed [21 / 21] Result: Complex[-1.2873764557791576, -1.1518291435850534] Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[1.1681841401903128, 0.11735444443083248] Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
22.6.E5	${\displaystyle{\displaystyle\operatorname{sn}\left(2z,k\right)=\frac{2% \operatorname{sn}\left(z,k\right)\operatorname{cn}\left(z,k\right)% \operatorname{dn}\left(z,k\right)}{1-k^{2}{\operatorname{sn}^{4}}\left(z,k% \right)}}}$ `\Jacobiellsnk@{2z}{k} = \frac{2\Jacobiellsnk@{z}{k}\Jacobiellcnk@{z}{k}\Jacobielldnk@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}}`	JacobiSN(2z, k) = (2JacobiSN(z, k)JacobiCN(z, k)JacobiDN(z, k))/(1 - (k)^(2)* (JacobiSN(z, k))^(4))	JacobiSN[2z, (k)^2] == Divide[2JacobiSN[z, (k)^2]JacobiCN[z, (k)^2]JacobiDN[z, (k)^2],1 - (k)^(2)* (JacobiSN[z, (k)^2])^(4)]	Failure	Aborted	Successful [Tested: 21]	Successful [Tested: 21]
22.6.E6	${\displaystyle{\displaystyle\operatorname{cn}\left(2z,k\right)=\frac{{% \operatorname{cn}^{2}}\left(z,k\right)-{\operatorname{sn}^{2}}\left(z,k\right)% {\operatorname{dn}^{2}}\left(z,k\right)}{1-k^{2}{\operatorname{sn}^{4}}\left(z% ,k\right)}}}$ `\Jacobiellcnk@{2z}{k} = \frac{\Jacobiellcnk^{2}@{z}{k}-\Jacobiellsnk^{2}@{z}{k}\Jacobielldnk^{2}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}}`	JacobiCN(2z, k) = ((JacobiCN(z, k))^(2)- (JacobiSN(z, k))^(2) (JacobiDN(z, k))^(2))/(1 - (k)^(2)* (JacobiSN(z, k))^(4))	JacobiCN[2z, (k)^2] == Divide[(JacobiCN[z, (k)^2])^(2)- (JacobiSN[z, (k)^2])^(2) (JacobiDN[z, (k)^2])^(2),1 - (k)^(2)* (JacobiSN[z, (k)^2])^(4)]	Failure	Aborted	Successful [Tested: 21]	Successful [Tested: 21]
22.6.E6	${\displaystyle{\displaystyle\frac{{\operatorname{cn}^{2}}\left(z,k\right)-{% \operatorname{sn}^{2}}\left(z,k\right){\operatorname{dn}^{2}}\left(z,k\right)}% {1-k^{2}{\operatorname{sn}^{4}}\left(z,k\right)}=\frac{{\operatorname{cn}^{4}}% \left(z,k\right)-{k^{\prime}}^{2}{\operatorname{sn}^{4}}\left(z,k\right)}{1-k^% {2}{\operatorname{sn}^{4}}\left(z,k\right)}}}$ `\frac{\Jacobiellcnk^{2}@{z}{k}-\Jacobiellsnk^{2}@{z}{k}\Jacobielldnk^{2}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}} = \frac{\Jacobiellcnk^{4}@{z}{k}-{k^{\prime}}^{2}\Jacobiellsnk^{4}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}}`	((JacobiCN(z, k))^(2)- (JacobiSN(z, k))^(2)* (JacobiDN(z, k))^(2))/(1 - (k)^(2)* (JacobiSN(z, k))^(4)) = ((JacobiCN(z, k))^(4)-1 - (k)^(2)(JacobiSN(z, k))^(4))/(1 - (k)^(2) (JacobiSN(z, k))^(4))	Divide[(JacobiCN[z, (k)^2])^(2)- (JacobiSN[z, (k)^2])^(2)* (JacobiDN[z, (k)^2])^(2),1 - (k)^(2)* (JacobiSN[z, (k)^2])^(4)] == Divide[(JacobiCN[z, (k)^2])^(4)-1 - (k)^(2)(JacobiSN[z, (k)^2])^(4),1 - (k)^(2) (JacobiSN[z, (k)^2])^(4)]	Failure	Failure	Failed [21 / 21] Result: .8884947272+1.003906290I Test Values: {z = 1/23^(1/2)+1/2I, k = 1} Result: 12.71128264-7.657522619I Test Values: {z = 1/23^(1/2)+1/2I, k = 2} ... skip entries to safe data	Failed [21 / 21] Result: Complex[0.88849472735544, 1.0039062900432163] Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[12.711282681655987, -7.657522555241993] Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
22.6.E7	${\displaystyle{\displaystyle\operatorname{dn}\left(2z,k\right)=\frac{{% \operatorname{dn}^{2}}\left(z,k\right)-k^{2}{\operatorname{sn}^{2}}\left(z,k% \right){\operatorname{cn}^{2}}\left(z,k\right)}{1-k^{2}{\operatorname{sn}^{4}}% \left(z,k\right)}}}$ `\Jacobielldnk@{2z}{k} = \frac{\Jacobielldnk^{2}@{z}{k}-k^{2}\Jacobiellsnk^{2}@{z}{k}\Jacobiellcnk^{2}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}}`	JacobiDN(2z, k) = ((JacobiDN(z, k))^(2)- (k)^(2) (JacobiSN(z, k))^(2)* (JacobiCN(z, k))^(2))/(1 - (k)^(2)* (JacobiSN(z, k))^(4))	JacobiDN[2z, (k)^2] == Divide[(JacobiDN[z, (k)^2])^(2)- (k)^(2) (JacobiSN[z, (k)^2])^(2)* (JacobiCN[z, (k)^2])^(2),1 - (k)^(2)* (JacobiSN[z, (k)^2])^(4)]	Failure	Aborted	Successful [Tested: 21]	Successful [Tested: 21]
22.6.E7	${\displaystyle{\displaystyle\frac{{\operatorname{dn}^{2}}\left(z,k\right)-k^{2% }{\operatorname{sn}^{2}}\left(z,k\right){\operatorname{cn}^{2}}\left(z,k\right% )}{1-k^{2}{\operatorname{sn}^{4}}\left(z,k\right)}=\frac{{\operatorname{dn}^{4% }}\left(z,k\right)+k^{2}{k^{\prime}}^{2}{\operatorname{sn}^{4}}\left(z,k\right% )}{1-k^{2}{\operatorname{sn}^{4}}\left(z,k\right)}}}$ `\frac{\Jacobielldnk^{2}@{z}{k}-k^{2}\Jacobiellsnk^{2}@{z}{k}\Jacobiellcnk^{2}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}} = \frac{\Jacobielldnk^{4}@{z}{k}+k^{2}{k^{\prime}}^{2}\Jacobiellsnk^{4}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}}`	((JacobiDN(z, k))^(2)- (k)^(2)* (JacobiSN(z, k))^(2)* (JacobiCN(z, k))^(2))/(1 - (k)^(2)* (JacobiSN(z, k))^(4)) = ((JacobiDN(z, k))^(4)+ (k)^(2)1 - (k)^(2)(JacobiSN(z, k))^(4))/(1 - (k)^(2)* (JacobiSN(z, k))^(4))	Divide[(JacobiDN[z, (k)^2])^(2)- (k)^(2)* (JacobiSN[z, (k)^2])^(2)* (JacobiCN[z, (k)^2])^(2),1 - (k)^(2)* (JacobiSN[z, (k)^2])^(4)] == Divide[(JacobiDN[z, (k)^2])^(4)+ (k)^(2)1 - (k)^(2)(JacobiSN[z, (k)^2])^(4),1 - (k)^(2)* (JacobiSN[z, (k)^2])^(4)]	Failure	Failure	Failed [21 / 21] Result: -1.000000000+0.I Test Values: {z = 1/23^(1/2)+1/2I, k = 1} Result: -29.55188938+16.70732208I Test Values: {z = 1/23^(1/2)+1/2I, k = 2} ... skip entries to safe data	Failed [21 / 21] Result: Complex[-1.0000000000000002, -1.1102230246251565*^-16] Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-29.55188948724943, 16.70732193870979] Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
22.6.E8	${\displaystyle{\displaystyle\operatorname{cd}\left(2z,k\right)=\frac{{% \operatorname{cd}^{2}}\left(z,k\right)-{k^{\prime}}^{2}{\operatorname{sd}^{2}}% \left(z,k\right){\operatorname{nd}^{2}}\left(z,k\right)}{1+k^{2}{k^{\prime}}^{% 2}{\operatorname{sd}^{4}}\left(z,k\right)}}}$ `\Jacobiellcdk@{2z}{k} = \frac{\Jacobiellcdk^{2}@{z}{k}-{k^{\prime}}^{2}\Jacobiellsdk^{2}@{z}{k}\Jacobiellndk^{2}@{z}{k}}{1+k^{2}{k^{\prime}}^{2}\Jacobiellsdk^{4}@{z}{k}}`	JacobiCD(2z, k) = ((JacobiCD(z, k))^(2)-1 - (k)^(2)(JacobiSD(z, k))^(2)* (JacobiND(z, k))^(2))/(1 + (k)^(2)1 - (k)^(2)(JacobiSD(z, k))^(4))	JacobiCD[2z, (k)^2] == Divide[(JacobiCD[z, (k)^2])^(2)-1 - (k)^(2)(JacobiSD[z, (k)^2])^(2)* (JacobiND[z, (k)^2])^(2),1 + (k)^(2)1 - (k)^(2)(JacobiSD[z, (k)^2])^(4)]	Failure	Aborted	Failed [21 / 21] Result: .6073373021+.4789879505I Test Values: {z = 1/23^(1/2)+1/2I, k = 1} Result: .5744703200+.1556450229I Test Values: {z = 1/23^(1/2)+1/2I, k = 2} ... skip entries to safe data	Failed [21 / 21] Result: Complex[0.6073373022896961, 0.47898795042922426] Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[0.5744703197186243, 0.15564502146829437] Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
22.6.E9	${\displaystyle{\displaystyle\operatorname{sd}\left(2z,k\right)=\frac{2% \operatorname{sd}\left(z,k\right)\operatorname{cd}\left(z,k\right)% \operatorname{nd}\left(z,k\right)}{1+k^{2}{k^{\prime}}^{2}{\operatorname{sd}^{% 4}}\left(z,k\right)}}}$ `\Jacobiellsdk@{2z}{k} = \frac{2\Jacobiellsdk@{z}{k}\Jacobiellcdk@{z}{k}\Jacobiellndk@{z}{k}}{1+k^{2}{k^{\prime}}^{2}\Jacobiellsdk^{4}@{z}{k}}`	JacobiSD(2z, k) = (2JacobiSD(z, k)JacobiCD(z, k)JacobiND(z, k))/(1 + (k)^(2)1 - (k)^(2)(JacobiSD(z, k))^(4))	JacobiSD[2z, (k)^2] == Divide[2JacobiSD[z, (k)^2]JacobiCD[z, (k)^2]JacobiND[z, (k)^2],1 + (k)^(2)1 - (k)^(2)(JacobiSD[z, (k)^2])^(4)]	Failure	Aborted	Failed [21 / 21] Result: 1.189544202+1.637439170I Test Values: {z = 1/23^(1/2)+1/2I, k = 1} Result: -.5756484648e-1+.8251147581I Test Values: {z = 1/23^(1/2)+1/2I, k = 2} ... skip entries to safe data	Failed [21 / 21] Result: Complex[1.189544200468709, 1.6374391687321102] Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-0.05756484595277844, 0.825114758131751] Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
22.6.E10	${\displaystyle{\displaystyle\operatorname{nd}\left(2z,k\right)=\frac{{% \operatorname{nd}^{2}}\left(z,k\right)+k^{2}{\operatorname{sd}^{2}}\left(z,k% \right){\operatorname{cd}^{2}}\left(z,k\right)}{1+k^{2}{k^{\prime}}^{2}{% \operatorname{sd}^{4}}\left(z,k\right)}}}$ `\Jacobiellndk@{2z}{k} = \frac{\Jacobiellndk^{2}@{z}{k}+k^{2}\Jacobiellsdk^{2}@{z}{k}\Jacobiellcdk^{2}@{z}{k}}{1+k^{2}{k^{\prime}}^{2}\Jacobiellsdk^{4}@{z}{k}}`	JacobiND(2z, k) = ((JacobiND(z, k))^(2)+ (k)^(2) (JacobiSD(z, k))^(2)* (JacobiCD(z, k))^(2))/(1 + (k)^(2)1 - (k)^(2)(JacobiSD(z, k))^(4))	JacobiND[2z, (k)^2] == Divide[(JacobiND[z, (k)^2])^(2)+ (k)^(2) (JacobiSD[z, (k)^2])^(2)* (JacobiCD[z, (k)^2])^(2),1 + (k)^(2)1 - (k)^(2)(JacobiSD[z, (k)^2])^(4)]	Failure	Aborted	Failed [21 / 21] Result: 1.247856974+1.526848242I Test Values: {z = 1/23^(1/2)+1/2I, k = 1} Result: -.1237018962-.8644962079e-1I Test Values: {z = 1/23^(1/2)+1/2I, k = 2} ... skip entries to safe data	Failed [21 / 21] Result: Complex[1.2478569728519586, 1.5268482411210251] Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-0.1237018961558749, -0.0864496199922923] Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
22.6.E11	${\displaystyle{\displaystyle\operatorname{dc}\left(2z,k\right)=\frac{{% \operatorname{dc}^{2}}\left(z,k\right)+{k^{\prime}}^{2}{\operatorname{sc}^{2}}% \left(z,k\right){\operatorname{nc}^{2}}\left(z,k\right)}{1-{k^{\prime}}^{2}{% \operatorname{sc}^{4}}\left(z,k\right)}}}$ `\Jacobielldck@{2z}{k} = \frac{\Jacobielldck^{2}@{z}{k}+{k^{\prime}}^{2}\Jacobiellsck^{2}@{z}{k}\Jacobiellnck^{2}@{z}{k}}{1-{k^{\prime}}^{2}\Jacobiellsck^{4}@{z}{k}}`	JacobiDC(2z, k) = ((JacobiDC(z, k))^(2)+1 - (k)^(2)(JacobiSC(z, k))^(2)* (JacobiNC(z, k))^(2))/(1 -1 - (k)^(2)*(JacobiSC(z, k))^(4))	JacobiDC[2z, (k)^2] == Divide[(JacobiDC[z, (k)^2])^(2)+1 - (k)^(2)(JacobiSC[z, (k)^2])^(2)* (JacobiNC[z, (k)^2])^(2),1 -1 - (k)^(2)*(JacobiSC[z, (k)^2])^(4)]	Failure	Aborted	Failed [21 / 21] Result: -1.456738398+.1506627644I Test Values: {z = 1/23^(1/2)+1/2I, k = 1} Result: -4.350355103-.3722352376e-1I Test Values: {z = 1/23^(1/2)+1/2I, k = 2} ... skip entries to safe data	Failed [21 / 21] Result: Complex[-1.456738400104645, 0.15066276425673586] Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-4.350355102633989, -0.03722352327899177] Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
22.6.E12	${\displaystyle{\displaystyle\operatorname{nc}\left(2z,k\right)=\frac{{% \operatorname{nc}^{2}}\left(z,k\right)+{\operatorname{sc}^{2}}\left(z,k\right)% {\operatorname{dc}^{2}}\left(z,k\right)}{1-{k^{\prime}}^{2}{\operatorname{sc}^% {4}}\left(z,k\right)}}}$ `\Jacobiellnck@{2z}{k} = \frac{\Jacobiellnck^{2}@{z}{k}+\Jacobiellsck^{2}@{z}{k}\Jacobielldck^{2}@{z}{k}}{1-{k^{\prime}}^{2}\Jacobiellsck^{4}@{z}{k}}`	JacobiNC(2z, k) = ((JacobiNC(z, k))^(2)+ (JacobiSC(z, k))^(2) (JacobiDC(z, k))^(2))/(1 -1 - (k)^(2)*(JacobiSC(z, k))^(4))	JacobiNC[2z, (k)^2] == Divide[(JacobiNC[z, (k)^2])^(2)+ (JacobiSC[z, (k)^2])^(2) (JacobiDC[z, (k)^2])^(2),1 -1 - (k)^(2)*(JacobiSC[z, (k)^2])^(4)]	Failure	Aborted	Failed [21 / 21] Result: 1.356171111+.335718656I Test Values: {z = 1/23^(1/2)+1/2I, k = 1} Result: .3210452605+.1984107752I Test Values: {z = 1/23^(1/2)+1/2I, k = 2} ... skip entries to safe data	Failed [21 / 21] Result: Complex[1.356171110076661, 0.3357186535359711] Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[0.3210452604978905, 0.19841077324251138] Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
22.6.E13	${\displaystyle{\displaystyle\operatorname{sc}\left(2z,k\right)=\frac{2% \operatorname{sc}\left(z,k\right)\operatorname{dc}\left(z,k\right)% \operatorname{nc}\left(z,k\right)}{1-{k^{\prime}}^{2}{\operatorname{sc}^{4}}% \left(z,k\right)}}}$ `\Jacobiellsck@{2z}{k} = \frac{2\Jacobiellsck@{z}{k}\Jacobielldck@{z}{k}\Jacobiellnck@{z}{k}}{1-{k^{\prime}}^{2}\Jacobiellsck^{4}@{z}{k}}`	JacobiSC(2z, k) = (2JacobiSC(z, k)JacobiDC(z, k)JacobiNC(z, k))/(1 -1 - (k)^(2)*(JacobiSC(z, k))^(4))	JacobiSC[2z, (k)^2] == Divide[2JacobiSC[z, (k)^2]JacobiDC[z, (k)^2]JacobiNC[z, (k)^2],1 -1 - (k)^(2)*(JacobiSC[z, (k)^2])^(4)]	Failure	Aborted	Failed [21 / 21] Result: 1.370082581+.423198902I Test Values: {z = 1/23^(1/2)+1/2I, k = 1} Result: .2742031773e-1-2.068263955I Test Values: {z = 1/23^(1/2)+1/2I, k = 2} ... skip entries to safe data	Failed [21 / 21] Result: Complex[1.3700825790735573, 0.42319889849983916] Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[0.027420317388659004, -2.068263954207401] Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
22.6.E14	${\displaystyle{\displaystyle\operatorname{ns}\left(2z,k\right)=\frac{{% \operatorname{ns}^{4}}\left(z,k\right)-k^{2}}{2\operatorname{cs}\left(z,k% \right)\operatorname{ds}\left(z,k\right)\operatorname{ns}\left(z,k\right)}}}$ `\Jacobiellnsk@{2z}{k} = \frac{\Jacobiellnsk^{4}@{z}{k}-k^{2}}{2\Jacobiellcsk@{z}{k}\Jacobielldsk@{z}{k}\Jacobiellnsk@{z}{k}}`	JacobiNS(2z, k) = ((JacobiNS(z, k))^(4)- (k)^(2))/(2JacobiCS(z, k)JacobiDS(z, k)JacobiNS(z, k))	JacobiNS[2z, (k)^2] == Divide[(JacobiNS[z, (k)^2])^(4)- (k)^(2),2JacobiCS[z, (k)^2]JacobiDS[z, (k)^2]JacobiNS[z, (k)^2]]	Failure	Aborted	Successful [Tested: 21]	Successful [Tested: 21]
22.6.E15	${\displaystyle{\displaystyle\operatorname{ds}\left(2z,k\right)=\frac{k^{2}{k^{% \prime}}^{2}+{\operatorname{ds}^{4}}\left(z,k\right)}{2\operatorname{cs}\left(% z,k\right)\operatorname{ds}\left(z,k\right)\operatorname{ns}\left(z,k\right)}}}$ `\Jacobielldsk@{2z}{k} = \frac{k^{2}{k^{\prime}}^{2}+\Jacobielldsk^{4}@{z}{k}}{2\Jacobiellcsk@{z}{k}\Jacobielldsk@{z}{k}\Jacobiellnsk@{z}{k}}`	JacobiDS(2z, k) = ((k)^(2)1 - (k)^(2)+ (JacobiDS(z, k))^(4))/(2JacobiCS(z, k)JacobiDS(z, k)*JacobiNS(z, k))	JacobiDS[2z, (k)^2] == Divide[(k)^(2)1 - (k)^(2)+ (JacobiDS[z, (k)^2])^(4),2JacobiCS[z, (k)^2]JacobiDS[z, (k)^2]*JacobiNS[z, (k)^2]]	Failure	Aborted	Failed [14 / 21] Result: -.1079800431-2.783083843I Test Values: {z = 1/23^(1/2)+1/2I, k = 2} Result: -6.118875072+.736498896I Test Values: {z = 1/23^(1/2)+1/2I, k = 3} ... skip entries to safe data	Failed [14 / 21] Result: Complex[-0.10798004208618706, -2.7830838428160787] Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-6.118875073385709, 0.7364988890066191] Test Values: {Rule[k, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
22.6.E16	${\displaystyle{\displaystyle\operatorname{cs}\left(2z,k\right)=\frac{{% \operatorname{cs}^{4}}\left(z,k\right)-{k^{\prime}}^{2}}{2\operatorname{cs}% \left(z,k\right)\operatorname{ds}\left(z,k\right)\operatorname{ns}\left(z,k% \right)}}}$ `\Jacobiellcsk@{2z}{k} = \frac{\Jacobiellcsk^{4}@{z}{k}-{k^{\prime}}^{2}}{2\Jacobiellcsk@{z}{k}\Jacobielldsk@{z}{k}\Jacobiellnsk@{z}{k}}`	JacobiCS(2z, k) = ((JacobiCS(z, k))^(4)-1 - (k)^(2))/(2JacobiCS(z, k)JacobiDS(z, k)JacobiNS(z, k))	JacobiCS[2z, (k)^2] == Divide[(JacobiCS[z, (k)^2])^(4)-1 - (k)^(2),2JacobiCS[z, (k)^2]JacobiDS[z, (k)^2]JacobiNS[z, (k)^2]]	Failure	Aborted	Failed [21 / 21] Result: -.528217681e-1+.9827060369I Test Values: {z = 1/23^(1/2)+1/2I, k = 1} Result: .7198669539e-1+1.855389227I Test Values: {z = 1/23^(1/2)+1/2I, k = 2} ... skip entries to safe data	Failed [21 / 21] Result: Complex[-0.05282176850410922, 0.9827060372847245] Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[0.07198669472412605, 1.8553892285440545] Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
22.6.E17	${\displaystyle{\displaystyle\frac{1-\operatorname{cn}\left(2z,k\right)}{1+% \operatorname{cn}\left(2z,k\right)}=\frac{{\operatorname{sn}^{2}}\left(z,k% \right){\operatorname{dn}^{2}}\left(z,k\right)}{{\operatorname{cn}^{2}}\left(z% ,k\right)}}}$ `\frac{1-\Jacobiellcnk@{2z}{k}}{1+\Jacobiellcnk@{2z}{k}} = \frac{\Jacobiellsnk^{2}@{z}{k}\Jacobielldnk^{2}@{z}{k}}{\Jacobiellcnk^{2}@{z}{k}}`	(1 - JacobiCN(2z, k))/(1 + JacobiCN(2z, k)) = ((JacobiSN(z, k))^(2)* (JacobiDN(z, k))^(2))/((JacobiCN(z, k))^(2))	Divide[1 - JacobiCN[2z, (k)^2],1 + JacobiCN[2z, (k)^2]] == Divide[(JacobiSN[z, (k)^2])^(2)* (JacobiDN[z, (k)^2])^(2),(JacobiCN[z, (k)^2])^(2)]	Failure	Aborted	Successful [Tested: 21]	Successful [Tested: 21]
22.6.E18	${\displaystyle{\displaystyle\frac{1-\operatorname{dn}\left(2z,k\right)}{1+% \operatorname{dn}\left(2z,k\right)}=\frac{k^{2}{\operatorname{sn}^{2}}\left(z,% k\right){\operatorname{cn}^{2}}\left(z,k\right)}{{\operatorname{dn}^{2}}\left(% z,k\right)}}}$ `\frac{1-\Jacobielldnk@{2z}{k}}{1+\Jacobielldnk@{2z}{k}} = \frac{k^{2}\Jacobiellsnk^{2}@{z}{k}\Jacobiellcnk^{2}@{z}{k}}{\Jacobielldnk^{2}@{z}{k}}`	(1 - JacobiDN(2z, k))/(1 + JacobiDN(2z, k)) = ((k)^(2)* (JacobiSN(z, k))^(2)* (JacobiCN(z, k))^(2))/((JacobiDN(z, k))^(2))	Divide[1 - JacobiDN[2z, (k)^2],1 + JacobiDN[2z, (k)^2]] == Divide[(k)^(2)* (JacobiSN[z, (k)^2])^(2)* (JacobiCN[z, (k)^2])^(2),(JacobiDN[z, (k)^2])^(2)]	Failure	Aborted	Successful [Tested: 21]	Successful [Tested: 21]
22.6.E19	${\displaystyle{\displaystyle{\operatorname{sn}^{2}}\left(\tfrac{1}{2}z,k\right% )=\frac{1-\operatorname{cn}\left(z,k\right)}{1+\operatorname{dn}\left(z,k% \right)}}}$ `\Jacobiellsnk^{2}@{\tfrac{1}{2}z}{k} = \frac{1-\Jacobiellcnk@{z}{k}}{1+\Jacobielldnk@{z}{k}}`	(JacobiSN((1)/(2)*z, k))^(2) = (1 - JacobiCN(z, k))/(1 + JacobiDN(z, k))	(JacobiSN[Divide[1,2]*z, (k)^2])^(2) == Divide[1 - JacobiCN[z, (k)^2],1 + JacobiDN[z, (k)^2]]	Failure	Aborted	Successful [Tested: 21]	Successful [Tested: 21]
22.6.E19	${\displaystyle{\displaystyle\frac{1-\operatorname{cn}\left(z,k\right)}{1+% \operatorname{dn}\left(z,k\right)}=\frac{1-\operatorname{dn}\left(z,k\right)}{% k^{2}(1+\operatorname{cn}\left(z,k\right))}}}$ `\frac{1-\Jacobiellcnk@{z}{k}}{1+\Jacobielldnk@{z}{k}} = \frac{1-\Jacobielldnk@{z}{k}}{k^{2}(1+\Jacobiellcnk@{z}{k})}`	(1 - JacobiCN(z, k))/(1 + JacobiDN(z, k)) = (1 - JacobiDN(z, k))/((k)^(2)*(1 + JacobiCN(z, k)))	Divide[1 - JacobiCN[z, (k)^2],1 + JacobiDN[z, (k)^2]] == Divide[1 - JacobiDN[z, (k)^2],(k)^(2)*(1 + JacobiCN[z, (k)^2])]	Successful	Successful	Skip - symbolical successful subtest	Successful [Tested: 21]
22.6.E19	${\displaystyle{\displaystyle\frac{1-\operatorname{dn}\left(z,k\right)}{k^{2}(1% +\operatorname{cn}\left(z,k\right))}=\frac{\operatorname{dn}\left(z,k\right)-k% ^{2}\operatorname{cn}\left(z,k\right)-{k^{\prime}}^{2}}{k^{2}(\operatorname{dn% }\left(z,k\right)-\operatorname{cn}\left(z,k\right))}}}$ `\frac{1-\Jacobielldnk@{z}{k}}{k^{2}(1+\Jacobiellcnk@{z}{k})} = \frac{\Jacobielldnk@{z}{k}-k^{2}\Jacobiellcnk@{z}{k}-{k^{\prime}}^{2}}{k^{2}(\Jacobielldnk@{z}{k}-\Jacobiellcnk@{z}{k})}`	(1 - JacobiDN(z, k))/((k)^(2)(1 + JacobiCN(z, k))) = (JacobiDN(z, k)- (k)^(2) JacobiCN(z, k)-1 - (k)^(2))/((k)^(2)*(JacobiDN(z, k)- JacobiCN(z, k)))	Divide[1 - JacobiDN[z, (k)^2],(k)^(2)(1 + JacobiCN[z, (k)^2])] == Divide[JacobiDN[z, (k)^2]- (k)^(2) JacobiCN[z, (k)^2]-1 - (k)^(2),(k)^(2)*(JacobiDN[z, (k)^2]- JacobiCN[z, (k)^2])]	Failure	Failure	Failed [21 / 21] Result: Float(infinity)+.1810063706I Test Values: {z = 1/23^(1/2)+1/2I, k = 1} Result: -1.050510101+1.261106800I Test Values: {z = 1/23^(1/2)+1/2I, k = 2} ... skip entries to safe data	Failed [21 / 21] Result: DirectedInfinity[] Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-1.0505101013872702, 1.2611068009765694] Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
22.6.E20	${\displaystyle{\displaystyle{\operatorname{cn}^{2}}\left(\tfrac{1}{2}z,k\right% )=\frac{-{k^{\prime}}^{2}+\operatorname{dn}\left(z,k\right)+k^{2}\operatorname% {cn}\left(z,k\right)}{k^{2}(1+\operatorname{cn}\left(z,k\right))}}}$ `\Jacobiellcnk^{2}@{\tfrac{1}{2}z}{k} = \frac{-{k^{\prime}}^{2}+\Jacobielldnk@{z}{k}+k^{2}\Jacobiellcnk@{z}{k}}{k^{2}(1+\Jacobiellcnk@{z}{k})}`	(JacobiCN((1)/(2)z, k))^(2) = (-1 - (k)^(2)+ JacobiDN(z, k)+ (k)^(2) JacobiCN(z, k))/((k)^(2)*(1 + JacobiCN(z, k)))	(JacobiCN[Divide[1,2]z, (k)^2])^(2) == Divide[-1 - (k)^(2)+ JacobiDN[z, (k)^2]+ (k)^(2) JacobiCN[z, (k)^2],(k)^(2)*(1 + JacobiCN[z, (k)^2])]	Failure	Aborted	Failed [21 / 21] Result: 1.140351911+.1810063706I Test Values: {z = 1/23^(1/2)+1/2I, k = 1} Result: 1.153509822-.96502865e-2I Test Values: {z = 1/23^(1/2)+1/2I, k = 2} ... skip entries to safe data	Failed [21 / 21] Result: Complex[1.140351911309134, 0.18100637055769858] Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[1.1535098215093709, -0.009650286433913441] Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
22.6.E20	${\displaystyle{\displaystyle\frac{-{k^{\prime}}^{2}+\operatorname{dn}\left(z,k% \right)+k^{2}\operatorname{cn}\left(z,k\right)}{k^{2}(1+\operatorname{cn}\left% (z,k\right))}=\frac{{k^{\prime}}^{2}(1-\operatorname{dn}\left(z,k\right))}{k^{% 2}(\operatorname{dn}\left(z,k\right)-\operatorname{cn}\left(z,k\right))}}}$ `\frac{-{k^{\prime}}^{2}+\Jacobielldnk@{z}{k}+k^{2}\Jacobiellcnk@{z}{k}}{k^{2}(1+\Jacobiellcnk@{z}{k})} = \frac{{k^{\prime}}^{2}(1-\Jacobielldnk@{z}{k})}{k^{2}(\Jacobielldnk@{z}{k}-\Jacobiellcnk@{z}{k})}`	(-1 - (k)^(2)+ JacobiDN(z, k)+ (k)^(2)* JacobiCN(z, k))/((k)^(2)(1 + JacobiCN(z, k))) = (1 - (k)^(2)(1 - JacobiDN(z, k)))/((k)^(2)*(JacobiDN(z, k)- JacobiCN(z, k)))	Divide[-1 - (k)^(2)+ JacobiDN[z, (k)^2]+ (k)^(2)* JacobiCN[z, (k)^2],(k)^(2)(1 + JacobiCN[z, (k)^2])] == Divide[1 - (k)^(2)(1 - JacobiDN[z, (k)^2]),(k)^(2)*(JacobiDN[z, (k)^2]- JacobiCN[z, (k)^2])]	Failure	Failure	Failed [21 / 21] Result: Float(infinity)+Float(infinity)I Test Values: {z = 1/23^(1/2)+1/2I, k = 1} Result: -1.304876195-.1041070951I Test Values: {z = 1/23^(1/2)+1/2I, k = 2} ... skip entries to safe data	Failed [21 / 21] Result: DirectedInfinity[] Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-1.304876194963382, -0.10410709518022829] Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
22.6.E20	${\displaystyle{\displaystyle\frac{{k^{\prime}}^{2}(1-\operatorname{dn}\left(z,% k\right))}{k^{2}(\operatorname{dn}\left(z,k\right)-\operatorname{cn}\left(z,k% \right))}=\frac{{k^{\prime}}^{2}(1+\operatorname{cn}\left(z,k\right))}{{k^{% \prime}}^{2}+\operatorname{dn}\left(z,k\right)-k^{2}\operatorname{cn}\left(z,k% \right)}}}$ `\frac{{k^{\prime}}^{2}(1-\Jacobielldnk@{z}{k})}{k^{2}(\Jacobielldnk@{z}{k}-\Jacobiellcnk@{z}{k})} = \frac{{k^{\prime}}^{2}(1+\Jacobiellcnk@{z}{k})}{{k^{\prime}}^{2}+\Jacobielldnk@{z}{k}-k^{2}\Jacobiellcnk@{z}{k}}`	(1 - (k)^(2)(1 - JacobiDN(z, k)))/((k)^(2)(JacobiDN(z, k)- JacobiCN(z, k))) = (1 - (k)^(2)(1 + JacobiCN(z, k)))/(1 - (k)^(2)+ JacobiDN(z, k)- (k)^(2) JacobiCN(z, k))	Divide[1 - (k)^(2)(1 - JacobiDN[z, (k)^2]),(k)^(2)(JacobiDN[z, (k)^2]- JacobiCN[z, (k)^2])] == Divide[1 - (k)^(2)(1 + JacobiCN[z, (k)^2]),1 - (k)^(2)+ JacobiDN[z, (k)^2]- (k)^(2) JacobiCN[z, (k)^2]]	Failure	Failure	Failed [21 / 21] Result: Float(infinity)-Float(infinity)I Test Values: {z = 1/23^(1/2)+1/2I, k = 1} Result: .315116621e-1+.1309658139I Test Values: {z = 1/23^(1/2)+1/2I, k = 2} ... skip entries to safe data	Failed [21 / 21] Result: Indeterminate Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[0.03151166205333389, 0.13096581390504758] Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
22.6.E21	${\displaystyle{\displaystyle{\operatorname{dn}^{2}}\left(\tfrac{1}{2}z,k\right% )=\frac{k^{2}\operatorname{cn}\left(z,k\right)+\operatorname{dn}\left(z,k% \right)+{k^{\prime}}^{2}}{1+\operatorname{dn}\left(z,k\right)}}}$ `\Jacobielldnk^{2}@{\tfrac{1}{2}z}{k} = \frac{k^{2}\Jacobiellcnk@{z}{k}+\Jacobielldnk@{z}{k}+{k^{\prime}}^{2}}{1+\Jacobielldnk@{z}{k}}`	(JacobiDN((1)/(2)z, k))^(2) = ((k)^(2) JacobiCN(z, k)+ JacobiDN(z, k)+1 - (k)^(2))/(1 + JacobiDN(z, k))	(JacobiDN[Divide[1,2]z, (k)^2])^(2) == Divide[(k)^(2) JacobiCN[z, (k)^2]+ JacobiDN[z, (k)^2]+1 - (k)^(2),1 + JacobiDN[z, (k)^2]]	Failure	Aborted	Successful [Tested: 21]	Successful [Tested: 21]
22.6.E21	${\displaystyle{\displaystyle\frac{k^{2}\operatorname{cn}\left(z,k\right)+% \operatorname{dn}\left(z,k\right)+{k^{\prime}}^{2}}{1+\operatorname{dn}\left(z% ,k\right)}=\frac{{k^{\prime}}^{2}(1-\operatorname{cn}\left(z,k\right))}{% \operatorname{dn}\left(z,k\right)-\operatorname{cn}\left(z,k\right)}}}$ `\frac{k^{2}\Jacobiellcnk@{z}{k}+\Jacobielldnk@{z}{k}+{k^{\prime}}^{2}}{1+\Jacobielldnk@{z}{k}} = \frac{{k^{\prime}}^{2}(1-\Jacobiellcnk@{z}{k})}{\Jacobielldnk@{z}{k}-\Jacobiellcnk@{z}{k}}`	((k)^(2)* JacobiCN(z, k)+ JacobiDN(z, k)+1 - (k)^(2))/(1 + JacobiDN(z, k)) = (1 - (k)^(2)*(1 - JacobiCN(z, k)))/(JacobiDN(z, k)- JacobiCN(z, k))	Divide[(k)^(2)* JacobiCN[z, (k)^2]+ JacobiDN[z, (k)^2]+1 - (k)^(2),1 + JacobiDN[z, (k)^2]] == Divide[1 - (k)^(2)*(1 - JacobiCN[z, (k)^2]),JacobiDN[z, (k)^2]- JacobiCN[z, (k)^2]]	Failure	Failure	Failed [21 / 21] Result: Float(infinity)+Float(infinity)I Test Values: {z = 1/23^(1/2)+1/2I, k = 1} Result: .3945345066-.4550295262I Test Values: {z = 1/23^(1/2)+1/2I, k = 2} ... skip entries to safe data	Failed [21 / 21] Result: DirectedInfinity[] Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[0.39453450618395575, -0.455029526456568] Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
22.6.E21	${\displaystyle{\displaystyle\frac{{k^{\prime}}^{2}(1-\operatorname{cn}\left(z,% k\right))}{\operatorname{dn}\left(z,k\right)-\operatorname{cn}\left(z,k\right)% }=\frac{{k^{\prime}}^{2}(1+\operatorname{dn}\left(z,k\right))}{{k^{\prime}}^{2% }+\operatorname{dn}\left(z,k\right)-k^{2}\operatorname{cn}\left(z,k\right)}}}$ `\frac{{k^{\prime}}^{2}(1-\Jacobiellcnk@{z}{k})}{\Jacobielldnk@{z}{k}-\Jacobiellcnk@{z}{k}} = \frac{{k^{\prime}}^{2}(1+\Jacobielldnk@{z}{k})}{{k^{\prime}}^{2}+\Jacobielldnk@{z}{k}-k^{2}\Jacobiellcnk@{z}{k}}`	(1 - (k)^(2)(1 - JacobiCN(z, k)))/(JacobiDN(z, k)- JacobiCN(z, k)) = (1 - (k)^(2)(1 + JacobiDN(z, k)))/(1 - (k)^(2)+ JacobiDN(z, k)- (k)^(2)* JacobiCN(z, k))	Divide[1 - (k)^(2)(1 - JacobiCN[z, (k)^2]),JacobiDN[z, (k)^2]- JacobiCN[z, (k)^2]] == Divide[1 - (k)^(2)(1 + JacobiDN[z, (k)^2]),1 - (k)^(2)+ JacobiDN[z, (k)^2]- (k)^(2)* JacobiCN[z, (k)^2]]	Failure	Failure	Failed [21 / 21] Result: Float(infinity)-Float(infinity)I Test Values: {z = 1/23^(1/2)+1/2I, k = 1} Result: -.3624296261+.6038808640I Test Values: {z = 1/23^(1/2)+1/2I, k = 2} ... skip entries to safe data	Failed [21 / 21] Result: Indeterminate Test Values: {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-0.3624296259668921, 0.6038808642712606] Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
22.6.E22	${\displaystyle{\displaystyle{\operatorname{pq}^{2}}\left(\tfrac{1}{2}z,k\right% )=\frac{\operatorname{ps}\left(z,k\right)+\operatorname{rs}\left(z,k\right)}{% \operatorname{qs}\left(z,k\right)+\operatorname{rs}\left(z,k\right)}}}$ `\genJacobiellk{p}{q}^{2}@{\tfrac{1}{2}z}{k} = \frac{\genJacobiellk{p}{s}@{z}{k}+\genJacobiellk{r}{s}@{z}{k}}{\genJacobiellk{q}{s}@{z}{k}+\genJacobiellk{r}{s}@{z}{k}}`	genJacobiellk(p)(q)^(2) (1)/(2)zk = (genJacobiellk(p)s* zk + genJacobiellk(r)s* zk)/(genJacobiellk(q)s* zk + genJacobiellk(r)s* z*k)	genJacobiellk[p](q)^(2) Divide[1,2]zk == Divide[genJacobiellk[p]s* zk + genJacobiellk[r]s* zk,genJacobiellk[q]s* zk + genJacobiellk[r]s* z*k]	Failure	Failure	Error	Failed [300 / 300] Result: Plus[Complex[-0.9999999999999999, -2.7755575615628914^-17], Times[Complex[0.0, 0.5], genJacobiellk, zk]] Test Values: {Rule[k, 1], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[r, -1.5], Rule[s, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Plus[Complex[-0.9999999999999999, -2.7755575615628914^-17], Times[Complex[0.0, 0.5], genJacobiellk, zk]] Test Values: {Rule[k, 2], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[r, -1.5], Rule[s, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
22.6.E22	${\displaystyle{\displaystyle\frac{\operatorname{ps}\left(z,k\right)+% \operatorname{rs}\left(z,k\right)}{\operatorname{qs}\left(z,k\right)+% \operatorname{rs}\left(z,k\right)}=\frac{\operatorname{pq}\left(z,k\right)+% \operatorname{rq}\left(z,k\right)}{1+\operatorname{rq}\left(z,k\right)}}}$ `\frac{\genJacobiellk{p}{s}@{z}{k}+\genJacobiellk{r}{s}@{z}{k}}{\genJacobiellk{q}{s}@{z}{k}+\genJacobiellk{r}{s}@{z}{k}} = \frac{\genJacobiellk{p}{q}@{z}{k}+\genJacobiellk{r}{q}@{z}{k}}{1+\genJacobiellk{r}{q}@{z}{k}}`	(genJacobiellk(p)s zk + genJacobiellk(r)s* zk)/(genJacobiellk(q)s* zk + genJacobiellk(r)s* zk) = (genJacobiellk(p)q* zk + genJacobiellk(r)q* zk)/(1 + genJacobiellk(r)q* z*k)	Divide[genJacobiellk[p]s zk + genJacobiellk[r]s* zk,genJacobiellk[q]s* zk + genJacobiellk[r]s* zk] == Divide[genJacobiellk[p]q* zk + genJacobiellk[r]q* zk,1 + genJacobiellk[r]q* z*k]	Failure	Failure	Error	Failed [300 / 300] Result: Plus[Complex[0.9999999999999999, 2.7755575615628914^-17], Times[Complex[0.7500000000000001, 0.2990381056766578], Power[Plus[1.0, Times[Complex[-0.7500000000000001, -1.2990381056766578], genJacobiellk]], -1], genJacobiellk]] Test Values: {Rule[k, 1], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[r, -1.5], Rule[s, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Plus[Complex[0.9999999999999999, 2.7755575615628914^-17], Times[Complex[1.5000000000000002, 0.5980762113533156], Power[Plus[1.0, Times[Complex[-1.5000000000000002, -2.5980762113533156], genJacobiellk]], -1], genJacobiellk]] Test Values: {Rule[k, 2], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[r, -1.5], Rule[s, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
22.6.E22	${\displaystyle{\displaystyle\frac{\operatorname{pq}\left(z,k\right)+% \operatorname{rq}\left(z,k\right)}{1+\operatorname{rq}\left(z,k\right)}=\frac{% \operatorname{pr}\left(z,k\right)+1}{\operatorname{qr}\left(z,k\right)+1}}}$ `\frac{\genJacobiellk{p}{q}@{z}{k}+\genJacobiellk{r}{q}@{z}{k}}{1+\genJacobiellk{r}{q}@{z}{k}} = \frac{\genJacobiellk{p}{r}@{z}{k}+1}{\genJacobiellk{q}{r}@{z}{k}+1}`	(genJacobiellk(p)q zk + genJacobiellk(r)q* zk)/(1 + genJacobiellk(r)q* zk) = (genJacobiellk(p)r* zk + 1)/(genJacobiellk(q)r* z*k + 1)	Divide[genJacobiellk[p]q zk + genJacobiellk[r]q* zk,1 + genJacobiellk[r]q* zk] == Divide[genJacobiellk[p]r* zk + 1,genJacobiellk[q]r* z*k + 1]	Failure	Failure	Error	Failed [300 / 300] Result: Plus[-1.0, Times[Complex[-0.7500000000000001, -0.2990381056766578], Power[Plus[1.0, Times[Complex[-0.7500000000000001, -1.2990381056766578], genJacobiellk]], -1], genJacobiellk]] Test Values: {Rule[k, 1], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[r, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Plus[-1.0, Times[Complex[-1.5000000000000002, -0.5980762113533156], Power[Plus[1.0, Times[Complex[-1.5000000000000002, -2.5980762113533156], genJacobiellk]], -1], genJacobiellk]] Test Values: {Rule[k, 2], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[r, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data

@@ Line 14: / Line 14: @@
 ! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
 |-
-| [https://dlmf.nist.gov/22.6.E1 22.6.E1] || [[Item:Q6935|<math>\Jacobiellsnk^{2}@{z}{k}+\Jacobiellcnk^{2}@{z}{k} = k^{2}\Jacobiellsnk^{2}@{z}{k}+\Jacobielldnk^{2}@{z}{k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellsnk^{2}@{z}{k}+\Jacobiellcnk^{2}@{z}{k} = k^{2}\Jacobiellsnk^{2}@{z}{k}+\Jacobielldnk^{2}@{z}{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(JacobiSN(z, k))^(2)+ (JacobiCN(z, k))^(2) = (k)^(2)* (JacobiSN(z, k))^(2)+ (JacobiDN(z, k))^(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(JacobiSN[z, (k)^2])^(2)+ (JacobiCN[z, (k)^2])^(2) == (k)^(2)* (JacobiSN[z, (k)^2])^(2)+ (JacobiDN[z, (k)^2])^(2)</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 21]
+| [https://dlmf.nist.gov/22.6.E1 22.6.E1] || <math qid="Q6935">\Jacobiellsnk^{2}@{z}{k}+\Jacobiellcnk^{2}@{z}{k} = k^{2}\Jacobiellsnk^{2}@{z}{k}+\Jacobielldnk^{2}@{z}{k}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellsnk^{2}@{z}{k}+\Jacobiellcnk^{2}@{z}{k} = k^{2}\Jacobiellsnk^{2}@{z}{k}+\Jacobielldnk^{2}@{z}{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(JacobiSN(z, k))^(2)+ (JacobiCN(z, k))^(2) = (k)^(2)* (JacobiSN(z, k))^(2)+ (JacobiDN(z, k))^(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(JacobiSN[z, (k)^2])^(2)+ (JacobiCN[z, (k)^2])^(2) == (k)^(2)* (JacobiSN[z, (k)^2])^(2)+ (JacobiDN[z, (k)^2])^(2)</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 21]
 |-
-| [https://dlmf.nist.gov/22.6.E1 22.6.E1] || [[Item:Q6935|<math>k^{2}\Jacobiellsnk^{2}@{z}{k}+\Jacobielldnk^{2}@{z}{k} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>k^{2}\Jacobiellsnk^{2}@{z}{k}+\Jacobielldnk^{2}@{z}{k} = 1</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(k)^(2)* (JacobiSN(z, k))^(2)+ (JacobiDN(z, k))^(2) = 1</syntaxhighlight> || <syntaxhighlight lang=mathematica>(k)^(2)* (JacobiSN[z, (k)^2])^(2)+ (JacobiDN[z, (k)^2])^(2) == 1</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 21]
+| [https://dlmf.nist.gov/22.6.E1 22.6.E1] || <math qid="Q6935">k^{2}\Jacobiellsnk^{2}@{z}{k}+\Jacobielldnk^{2}@{z}{k} = 1</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>k^{2}\Jacobiellsnk^{2}@{z}{k}+\Jacobielldnk^{2}@{z}{k} = 1</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(k)^(2)* (JacobiSN(z, k))^(2)+ (JacobiDN(z, k))^(2) = 1</syntaxhighlight> || <syntaxhighlight lang=mathematica>(k)^(2)* (JacobiSN[z, (k)^2])^(2)+ (JacobiDN[z, (k)^2])^(2) == 1</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 21]
 |-
-| [https://dlmf.nist.gov/22.6.E2 22.6.E2] || [[Item:Q6936|<math>1+\Jacobiellcsk^{2}@{z}{k} = k^{2}+\Jacobielldsk^{2}@{z}{k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>1+\Jacobiellcsk^{2}@{z}{k} = k^{2}+\Jacobielldsk^{2}@{z}{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>1 + (JacobiCS(z, k))^(2) = (k)^(2)+ (JacobiDS(z, k))^(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>1 + (JacobiCS[z, (k)^2])^(2) == (k)^(2)+ (JacobiDS[z, (k)^2])^(2)</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 21]
+| [https://dlmf.nist.gov/22.6.E2 22.6.E2] || <math qid="Q6936">1+\Jacobiellcsk^{2}@{z}{k} = k^{2}+\Jacobielldsk^{2}@{z}{k}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>1+\Jacobiellcsk^{2}@{z}{k} = k^{2}+\Jacobielldsk^{2}@{z}{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>1 + (JacobiCS(z, k))^(2) = (k)^(2)+ (JacobiDS(z, k))^(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>1 + (JacobiCS[z, (k)^2])^(2) == (k)^(2)+ (JacobiDS[z, (k)^2])^(2)</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 21]
 |-
-| [https://dlmf.nist.gov/22.6.E2 22.6.E2] || [[Item:Q6936|<math>k^{2}+\Jacobielldsk^{2}@{z}{k} = \Jacobiellnsk^{2}@{z}{k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>k^{2}+\Jacobielldsk^{2}@{z}{k} = \Jacobiellnsk^{2}@{z}{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(k)^(2)+ (JacobiDS(z, k))^(2) = (JacobiNS(z, k))^(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(k)^(2)+ (JacobiDS[z, (k)^2])^(2) == (JacobiNS[z, (k)^2])^(2)</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 21]
+| [https://dlmf.nist.gov/22.6.E2 22.6.E2] || <math qid="Q6936">k^{2}+\Jacobielldsk^{2}@{z}{k} = \Jacobiellnsk^{2}@{z}{k}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>k^{2}+\Jacobielldsk^{2}@{z}{k} = \Jacobiellnsk^{2}@{z}{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(k)^(2)+ (JacobiDS(z, k))^(2) = (JacobiNS(z, k))^(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(k)^(2)+ (JacobiDS[z, (k)^2])^(2) == (JacobiNS[z, (k)^2])^(2)</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 21]
 |-
-| [https://dlmf.nist.gov/22.6.E3 22.6.E3] || [[Item:Q6937|<math>{k^{\prime}}^{2}\Jacobiellsck^{2}@{z}{k}+1 = \Jacobielldck^{2}@{z}{k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>{k^{\prime}}^{2}\Jacobiellsck^{2}@{z}{k}+1 = \Jacobielldck^{2}@{z}{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>1 - (k)^(2)*(JacobiSC(z, k))^(2)+ 1 = (JacobiDC(z, k))^(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>1 - (k)^(2)*(JacobiSC[z, (k)^2])^(2)+ 1 == (JacobiDC[z, (k)^2])^(2)</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .7126235439-1.151829144*I
+| [https://dlmf.nist.gov/22.6.E3 22.6.E3] || <math qid="Q6937">{k^{\prime}}^{2}\Jacobiellsck^{2}@{z}{k}+1 = \Jacobielldck^{2}@{z}{k}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>{k^{\prime}}^{2}\Jacobiellsck^{2}@{z}{k}+1 = \Jacobielldck^{2}@{z}{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>1 - (k)^(2)*(JacobiSC(z, k))^(2)+ 1 = (JacobiDC(z, k))^(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>1 - (k)^(2)*(JacobiSC[z, (k)^2])^(2)+ 1 == (JacobiDC[z, (k)^2])^(2)</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .7126235439-1.151829144*I
 Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .144618294+.733840068e-1*I
 Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.7126235442208428, -1.1518291435850532]
@@ Line 28: / Line 28: @@
 Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/22.6.E3 22.6.E3] || [[Item:Q6937|<math>\Jacobielldck^{2}@{z}{k} = {k^{\prime}}^{2}\Jacobiellnck^{2}@{z}{k}+k^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobielldck^{2}@{z}{k} = {k^{\prime}}^{2}\Jacobiellnck^{2}@{z}{k}+k^{2}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(JacobiDC(z, k))^(2) = 1 - (k)^(2)*(JacobiNC(z, k))^(2)+ (k)^(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(JacobiDC[z, (k)^2])^(2) == 1 - (k)^(2)*(JacobiNC[z, (k)^2])^(2)+ (k)^(2)</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .287376456+1.151829144*I
+| [https://dlmf.nist.gov/22.6.E3 22.6.E3] || <math qid="Q6937">\Jacobielldck^{2}@{z}{k} = {k^{\prime}}^{2}\Jacobiellnck^{2}@{z}{k}+k^{2}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobielldck^{2}@{z}{k} = {k^{\prime}}^{2}\Jacobiellnck^{2}@{z}{k}+k^{2}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(JacobiDC(z, k))^(2) = 1 - (k)^(2)*(JacobiNC(z, k))^(2)+ (k)^(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(JacobiDC[z, (k)^2])^(2) == 1 - (k)^(2)*(JacobiNC[z, (k)^2])^(2)+ (k)^(2)</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .287376456+1.151829144*I
 Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .855381706-.733840068e-1*I
 Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.0
@@ Line 34: / Line 34: @@
 Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/22.6.E4 22.6.E4] || [[Item:Q6938|<math>-k^{2}{k^{\prime}}^{2}\Jacobiellsdk^{2}@{z}{k} = k^{2}(\Jacobiellcdk^{2}@{z}{k}-1)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>-k^{2}{k^{\prime}}^{2}\Jacobiellsdk^{2}@{z}{k} = k^{2}(\Jacobiellcdk^{2}@{z}{k}-1)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>- (k)^(2)*1 - (k)^(2)*(JacobiSD(z, k))^(2) = (k)^(2)*((JacobiCD(z, k))^(2)- 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>- (k)^(2)*1 - (k)^(2)*(JacobiSD[z, (k)^2])^(2) == (k)^(2)*((JacobiCD[z, (k)^2])^(2)- 1)</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.287376456-1.151829144*I
+| [https://dlmf.nist.gov/22.6.E4 22.6.E4] || <math qid="Q6938">-k^{2}{k^{\prime}}^{2}\Jacobiellsdk^{2}@{z}{k} = k^{2}(\Jacobiellcdk^{2}@{z}{k}-1)</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>-k^{2}{k^{\prime}}^{2}\Jacobiellsdk^{2}@{z}{k} = k^{2}(\Jacobiellcdk^{2}@{z}{k}-1)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>- (k)^(2)*1 - (k)^(2)*(JacobiSD(z, k))^(2) = (k)^(2)*((JacobiCD(z, k))^(2)- 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>- (k)^(2)*1 - (k)^(2)*(JacobiSD[z, (k)^2])^(2) == (k)^(2)*((JacobiCD[z, (k)^2])^(2)- 1)</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.287376456-1.151829144*I
 Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 4.672736560+.4694177821*I
 Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-1.2873764557791572, -1.1518291435850532]
@@ Line 40: / Line 40: @@
 Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/22.6.E4 22.6.E4] || [[Item:Q6938|<math>k^{2}(\Jacobiellcdk^{2}@{z}{k}-1) = {k^{\prime}}^{2}(1-\Jacobiellndk^{2}@{z}{k})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>k^{2}(\Jacobiellcdk^{2}@{z}{k}-1) = {k^{\prime}}^{2}(1-\Jacobiellndk^{2}@{z}{k})</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(k)^(2)*((JacobiCD(z, k))^(2)- 1) = 1 - (k)^(2)*(1 - (JacobiND(z, k))^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(k)^(2)*((JacobiCD[z, (k)^2])^(2)- 1) == 1 - (k)^(2)*(1 - (JacobiND[z, (k)^2])^(2))</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.287376456-1.151829144*I
+| [https://dlmf.nist.gov/22.6.E4 22.6.E4] || <math qid="Q6938">k^{2}(\Jacobiellcdk^{2}@{z}{k}-1) = {k^{\prime}}^{2}(1-\Jacobiellndk^{2}@{z}{k})</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>k^{2}(\Jacobiellcdk^{2}@{z}{k}-1) = {k^{\prime}}^{2}(1-\Jacobiellndk^{2}@{z}{k})</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(k)^(2)*((JacobiCD(z, k))^(2)- 1) = 1 - (k)^(2)*(1 - (JacobiND(z, k))^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(k)^(2)*((JacobiCD[z, (k)^2])^(2)- 1) == 1 - (k)^(2)*(1 - (JacobiND[z, (k)^2])^(2))</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.287376456-1.151829144*I
 Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.168184140+.1173544454*I
 Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-1.2873764557791576, -1.1518291435850534]
@@ Line 46: / Line 46: @@
 Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/22.6.E5 22.6.E5] || [[Item:Q6939|<math>\Jacobiellsnk@{2z}{k} = \frac{2\Jacobiellsnk@{z}{k}\Jacobiellcnk@{z}{k}\Jacobielldnk@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellsnk@{2z}{k} = \frac{2\Jacobiellsnk@{z}{k}\Jacobiellcnk@{z}{k}\Jacobielldnk@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiSN(2*z, k) = (2*JacobiSN(z, k)*JacobiCN(z, k)*JacobiDN(z, k))/(1 - (k)^(2)* (JacobiSN(z, k))^(4))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiSN[2*z, (k)^2] == Divide[2*JacobiSN[z, (k)^2]*JacobiCN[z, (k)^2]*JacobiDN[z, (k)^2],1 - (k)^(2)* (JacobiSN[z, (k)^2])^(4)]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 21] || Successful [Tested: 21]
+| [https://dlmf.nist.gov/22.6.E5 22.6.E5] || <math qid="Q6939">\Jacobiellsnk@{2z}{k} = \frac{2\Jacobiellsnk@{z}{k}\Jacobiellcnk@{z}{k}\Jacobielldnk@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellsnk@{2z}{k} = \frac{2\Jacobiellsnk@{z}{k}\Jacobiellcnk@{z}{k}\Jacobielldnk@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiSN(2*z, k) = (2*JacobiSN(z, k)*JacobiCN(z, k)*JacobiDN(z, k))/(1 - (k)^(2)* (JacobiSN(z, k))^(4))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiSN[2*z, (k)^2] == Divide[2*JacobiSN[z, (k)^2]*JacobiCN[z, (k)^2]*JacobiDN[z, (k)^2],1 - (k)^(2)* (JacobiSN[z, (k)^2])^(4)]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 21] || Successful [Tested: 21]
 |-
-| [https://dlmf.nist.gov/22.6.E6 22.6.E6] || [[Item:Q6940|<math>\Jacobiellcnk@{2z}{k} = \frac{\Jacobiellcnk^{2}@{z}{k}-\Jacobiellsnk^{2}@{z}{k}\Jacobielldnk^{2}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellcnk@{2z}{k} = \frac{\Jacobiellcnk^{2}@{z}{k}-\Jacobiellsnk^{2}@{z}{k}\Jacobielldnk^{2}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiCN(2*z, k) = ((JacobiCN(z, k))^(2)- (JacobiSN(z, k))^(2)* (JacobiDN(z, k))^(2))/(1 - (k)^(2)* (JacobiSN(z, k))^(4))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiCN[2*z, (k)^2] == Divide[(JacobiCN[z, (k)^2])^(2)- (JacobiSN[z, (k)^2])^(2)* (JacobiDN[z, (k)^2])^(2),1 - (k)^(2)* (JacobiSN[z, (k)^2])^(4)]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 21] || Successful [Tested: 21]
+| [https://dlmf.nist.gov/22.6.E6 22.6.E6] || <math qid="Q6940">\Jacobiellcnk@{2z}{k} = \frac{\Jacobiellcnk^{2}@{z}{k}-\Jacobiellsnk^{2}@{z}{k}\Jacobielldnk^{2}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellcnk@{2z}{k} = \frac{\Jacobiellcnk^{2}@{z}{k}-\Jacobiellsnk^{2}@{z}{k}\Jacobielldnk^{2}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiCN(2*z, k) = ((JacobiCN(z, k))^(2)- (JacobiSN(z, k))^(2)* (JacobiDN(z, k))^(2))/(1 - (k)^(2)* (JacobiSN(z, k))^(4))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiCN[2*z, (k)^2] == Divide[(JacobiCN[z, (k)^2])^(2)- (JacobiSN[z, (k)^2])^(2)* (JacobiDN[z, (k)^2])^(2),1 - (k)^(2)* (JacobiSN[z, (k)^2])^(4)]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 21] || Successful [Tested: 21]
 |-
-| [https://dlmf.nist.gov/22.6.E6 22.6.E6] || [[Item:Q6940|<math>\frac{\Jacobiellcnk^{2}@{z}{k}-\Jacobiellsnk^{2}@{z}{k}\Jacobielldnk^{2}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}} = \frac{\Jacobiellcnk^{4}@{z}{k}-{k^{\prime}}^{2}\Jacobiellsnk^{4}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{\Jacobiellcnk^{2}@{z}{k}-\Jacobiellsnk^{2}@{z}{k}\Jacobielldnk^{2}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}} = \frac{\Jacobiellcnk^{4}@{z}{k}-{k^{\prime}}^{2}\Jacobiellsnk^{4}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>((JacobiCN(z, k))^(2)- (JacobiSN(z, k))^(2)* (JacobiDN(z, k))^(2))/(1 - (k)^(2)* (JacobiSN(z, k))^(4)) = ((JacobiCN(z, k))^(4)-1 - (k)^(2)*(JacobiSN(z, k))^(4))/(1 - (k)^(2)* (JacobiSN(z, k))^(4))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[(JacobiCN[z, (k)^2])^(2)- (JacobiSN[z, (k)^2])^(2)* (JacobiDN[z, (k)^2])^(2),1 - (k)^(2)* (JacobiSN[z, (k)^2])^(4)] == Divide[(JacobiCN[z, (k)^2])^(4)-1 - (k)^(2)*(JacobiSN[z, (k)^2])^(4),1 - (k)^(2)* (JacobiSN[z, (k)^2])^(4)]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .8884947272+1.003906290*I
+| [https://dlmf.nist.gov/22.6.E6 22.6.E6] || <math qid="Q6940">\frac{\Jacobiellcnk^{2}@{z}{k}-\Jacobiellsnk^{2}@{z}{k}\Jacobielldnk^{2}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}} = \frac{\Jacobiellcnk^{4}@{z}{k}-{k^{\prime}}^{2}\Jacobiellsnk^{4}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{\Jacobiellcnk^{2}@{z}{k}-\Jacobiellsnk^{2}@{z}{k}\Jacobielldnk^{2}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}} = \frac{\Jacobiellcnk^{4}@{z}{k}-{k^{\prime}}^{2}\Jacobiellsnk^{4}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>((JacobiCN(z, k))^(2)- (JacobiSN(z, k))^(2)* (JacobiDN(z, k))^(2))/(1 - (k)^(2)* (JacobiSN(z, k))^(4)) = ((JacobiCN(z, k))^(4)-1 - (k)^(2)*(JacobiSN(z, k))^(4))/(1 - (k)^(2)* (JacobiSN(z, k))^(4))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[(JacobiCN[z, (k)^2])^(2)- (JacobiSN[z, (k)^2])^(2)* (JacobiDN[z, (k)^2])^(2),1 - (k)^(2)* (JacobiSN[z, (k)^2])^(4)] == Divide[(JacobiCN[z, (k)^2])^(4)-1 - (k)^(2)*(JacobiSN[z, (k)^2])^(4),1 - (k)^(2)* (JacobiSN[z, (k)^2])^(4)]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .8884947272+1.003906290*I
 Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 12.71128264-7.657522619*I
 Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.88849472735544, 1.0039062900432163]
@@ Line 56: / Line 56: @@
 Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/22.6.E7 22.6.E7] || [[Item:Q6941|<math>\Jacobielldnk@{2z}{k} = \frac{\Jacobielldnk^{2}@{z}{k}-k^{2}\Jacobiellsnk^{2}@{z}{k}\Jacobiellcnk^{2}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobielldnk@{2z}{k} = \frac{\Jacobielldnk^{2}@{z}{k}-k^{2}\Jacobiellsnk^{2}@{z}{k}\Jacobiellcnk^{2}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiDN(2*z, k) = ((JacobiDN(z, k))^(2)- (k)^(2)* (JacobiSN(z, k))^(2)* (JacobiCN(z, k))^(2))/(1 - (k)^(2)* (JacobiSN(z, k))^(4))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiDN[2*z, (k)^2] == Divide[(JacobiDN[z, (k)^2])^(2)- (k)^(2)* (JacobiSN[z, (k)^2])^(2)* (JacobiCN[z, (k)^2])^(2),1 - (k)^(2)* (JacobiSN[z, (k)^2])^(4)]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 21] || Successful [Tested: 21]
+| [https://dlmf.nist.gov/22.6.E7 22.6.E7] || <math qid="Q6941">\Jacobielldnk@{2z}{k} = \frac{\Jacobielldnk^{2}@{z}{k}-k^{2}\Jacobiellsnk^{2}@{z}{k}\Jacobiellcnk^{2}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobielldnk@{2z}{k} = \frac{\Jacobielldnk^{2}@{z}{k}-k^{2}\Jacobiellsnk^{2}@{z}{k}\Jacobiellcnk^{2}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiDN(2*z, k) = ((JacobiDN(z, k))^(2)- (k)^(2)* (JacobiSN(z, k))^(2)* (JacobiCN(z, k))^(2))/(1 - (k)^(2)* (JacobiSN(z, k))^(4))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiDN[2*z, (k)^2] == Divide[(JacobiDN[z, (k)^2])^(2)- (k)^(2)* (JacobiSN[z, (k)^2])^(2)* (JacobiCN[z, (k)^2])^(2),1 - (k)^(2)* (JacobiSN[z, (k)^2])^(4)]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 21] || Successful [Tested: 21]
 |-
-| [https://dlmf.nist.gov/22.6.E7 22.6.E7] || [[Item:Q6941|<math>\frac{\Jacobielldnk^{2}@{z}{k}-k^{2}\Jacobiellsnk^{2}@{z}{k}\Jacobiellcnk^{2}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}} = \frac{\Jacobielldnk^{4}@{z}{k}+k^{2}{k^{\prime}}^{2}\Jacobiellsnk^{4}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{\Jacobielldnk^{2}@{z}{k}-k^{2}\Jacobiellsnk^{2}@{z}{k}\Jacobiellcnk^{2}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}} = \frac{\Jacobielldnk^{4}@{z}{k}+k^{2}{k^{\prime}}^{2}\Jacobiellsnk^{4}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>((JacobiDN(z, k))^(2)- (k)^(2)* (JacobiSN(z, k))^(2)* (JacobiCN(z, k))^(2))/(1 - (k)^(2)* (JacobiSN(z, k))^(4)) = ((JacobiDN(z, k))^(4)+ (k)^(2)*1 - (k)^(2)*(JacobiSN(z, k))^(4))/(1 - (k)^(2)* (JacobiSN(z, k))^(4))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[(JacobiDN[z, (k)^2])^(2)- (k)^(2)* (JacobiSN[z, (k)^2])^(2)* (JacobiCN[z, (k)^2])^(2),1 - (k)^(2)* (JacobiSN[z, (k)^2])^(4)] == Divide[(JacobiDN[z, (k)^2])^(4)+ (k)^(2)*1 - (k)^(2)*(JacobiSN[z, (k)^2])^(4),1 - (k)^(2)* (JacobiSN[z, (k)^2])^(4)]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.000000000+0.*I
+| [https://dlmf.nist.gov/22.6.E7 22.6.E7] || <math qid="Q6941">\frac{\Jacobielldnk^{2}@{z}{k}-k^{2}\Jacobiellsnk^{2}@{z}{k}\Jacobiellcnk^{2}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}} = \frac{\Jacobielldnk^{4}@{z}{k}+k^{2}{k^{\prime}}^{2}\Jacobiellsnk^{4}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{\Jacobielldnk^{2}@{z}{k}-k^{2}\Jacobiellsnk^{2}@{z}{k}\Jacobiellcnk^{2}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}} = \frac{\Jacobielldnk^{4}@{z}{k}+k^{2}{k^{\prime}}^{2}\Jacobiellsnk^{4}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>((JacobiDN(z, k))^(2)- (k)^(2)* (JacobiSN(z, k))^(2)* (JacobiCN(z, k))^(2))/(1 - (k)^(2)* (JacobiSN(z, k))^(4)) = ((JacobiDN(z, k))^(4)+ (k)^(2)*1 - (k)^(2)*(JacobiSN(z, k))^(4))/(1 - (k)^(2)* (JacobiSN(z, k))^(4))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[(JacobiDN[z, (k)^2])^(2)- (k)^(2)* (JacobiSN[z, (k)^2])^(2)* (JacobiCN[z, (k)^2])^(2),1 - (k)^(2)* (JacobiSN[z, (k)^2])^(4)] == Divide[(JacobiDN[z, (k)^2])^(4)+ (k)^(2)*1 - (k)^(2)*(JacobiSN[z, (k)^2])^(4),1 - (k)^(2)* (JacobiSN[z, (k)^2])^(4)]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.000000000+0.*I
 Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -29.55188938+16.70732208*I
 Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-1.0000000000000002, -1.1102230246251565*^-16]
@@ Line 64: / Line 64: @@
 Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/22.6.E8 22.6.E8] || [[Item:Q6942|<math>\Jacobiellcdk@{2z}{k} = \frac{\Jacobiellcdk^{2}@{z}{k}-{k^{\prime}}^{2}\Jacobiellsdk^{2}@{z}{k}\Jacobiellndk^{2}@{z}{k}}{1+k^{2}{k^{\prime}}^{2}\Jacobiellsdk^{4}@{z}{k}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellcdk@{2z}{k} = \frac{\Jacobiellcdk^{2}@{z}{k}-{k^{\prime}}^{2}\Jacobiellsdk^{2}@{z}{k}\Jacobiellndk^{2}@{z}{k}}{1+k^{2}{k^{\prime}}^{2}\Jacobiellsdk^{4}@{z}{k}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiCD(2*z, k) = ((JacobiCD(z, k))^(2)-1 - (k)^(2)*(JacobiSD(z, k))^(2)* (JacobiND(z, k))^(2))/(1 + (k)^(2)*1 - (k)^(2)*(JacobiSD(z, k))^(4))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiCD[2*z, (k)^2] == Divide[(JacobiCD[z, (k)^2])^(2)-1 - (k)^(2)*(JacobiSD[z, (k)^2])^(2)* (JacobiND[z, (k)^2])^(2),1 + (k)^(2)*1 - (k)^(2)*(JacobiSD[z, (k)^2])^(4)]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .6073373021+.4789879505*I
+| [https://dlmf.nist.gov/22.6.E8 22.6.E8] || <math qid="Q6942">\Jacobiellcdk@{2z}{k} = \frac{\Jacobiellcdk^{2}@{z}{k}-{k^{\prime}}^{2}\Jacobiellsdk^{2}@{z}{k}\Jacobiellndk^{2}@{z}{k}}{1+k^{2}{k^{\prime}}^{2}\Jacobiellsdk^{4}@{z}{k}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellcdk@{2z}{k} = \frac{\Jacobiellcdk^{2}@{z}{k}-{k^{\prime}}^{2}\Jacobiellsdk^{2}@{z}{k}\Jacobiellndk^{2}@{z}{k}}{1+k^{2}{k^{\prime}}^{2}\Jacobiellsdk^{4}@{z}{k}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiCD(2*z, k) = ((JacobiCD(z, k))^(2)-1 - (k)^(2)*(JacobiSD(z, k))^(2)* (JacobiND(z, k))^(2))/(1 + (k)^(2)*1 - (k)^(2)*(JacobiSD(z, k))^(4))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiCD[2*z, (k)^2] == Divide[(JacobiCD[z, (k)^2])^(2)-1 - (k)^(2)*(JacobiSD[z, (k)^2])^(2)* (JacobiND[z, (k)^2])^(2),1 + (k)^(2)*1 - (k)^(2)*(JacobiSD[z, (k)^2])^(4)]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .6073373021+.4789879505*I
 Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .5744703200+.1556450229*I
 Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.6073373022896961, 0.47898795042922426]
@@ Line 70: / Line 70: @@
 Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/22.6.E9 22.6.E9] || [[Item:Q6943|<math>\Jacobiellsdk@{2z}{k} = \frac{2\Jacobiellsdk@{z}{k}\Jacobiellcdk@{z}{k}\Jacobiellndk@{z}{k}}{1+k^{2}{k^{\prime}}^{2}\Jacobiellsdk^{4}@{z}{k}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellsdk@{2z}{k} = \frac{2\Jacobiellsdk@{z}{k}\Jacobiellcdk@{z}{k}\Jacobiellndk@{z}{k}}{1+k^{2}{k^{\prime}}^{2}\Jacobiellsdk^{4}@{z}{k}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiSD(2*z, k) = (2*JacobiSD(z, k)*JacobiCD(z, k)*JacobiND(z, k))/(1 + (k)^(2)*1 - (k)^(2)*(JacobiSD(z, k))^(4))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiSD[2*z, (k)^2] == Divide[2*JacobiSD[z, (k)^2]*JacobiCD[z, (k)^2]*JacobiND[z, (k)^2],1 + (k)^(2)*1 - (k)^(2)*(JacobiSD[z, (k)^2])^(4)]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.189544202+1.637439170*I
+| [https://dlmf.nist.gov/22.6.E9 22.6.E9] || <math qid="Q6943">\Jacobiellsdk@{2z}{k} = \frac{2\Jacobiellsdk@{z}{k}\Jacobiellcdk@{z}{k}\Jacobiellndk@{z}{k}}{1+k^{2}{k^{\prime}}^{2}\Jacobiellsdk^{4}@{z}{k}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellsdk@{2z}{k} = \frac{2\Jacobiellsdk@{z}{k}\Jacobiellcdk@{z}{k}\Jacobiellndk@{z}{k}}{1+k^{2}{k^{\prime}}^{2}\Jacobiellsdk^{4}@{z}{k}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiSD(2*z, k) = (2*JacobiSD(z, k)*JacobiCD(z, k)*JacobiND(z, k))/(1 + (k)^(2)*1 - (k)^(2)*(JacobiSD(z, k))^(4))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiSD[2*z, (k)^2] == Divide[2*JacobiSD[z, (k)^2]*JacobiCD[z, (k)^2]*JacobiND[z, (k)^2],1 + (k)^(2)*1 - (k)^(2)*(JacobiSD[z, (k)^2])^(4)]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.189544202+1.637439170*I
 Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.5756484648e-1+.8251147581*I
 Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.189544200468709, 1.6374391687321102]
@@ Line 76: / Line 76: @@
 Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/22.6.E10 22.6.E10] || [[Item:Q6944|<math>\Jacobiellndk@{2z}{k} = \frac{\Jacobiellndk^{2}@{z}{k}+k^{2}\Jacobiellsdk^{2}@{z}{k}\Jacobiellcdk^{2}@{z}{k}}{1+k^{2}{k^{\prime}}^{2}\Jacobiellsdk^{4}@{z}{k}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellndk@{2z}{k} = \frac{\Jacobiellndk^{2}@{z}{k}+k^{2}\Jacobiellsdk^{2}@{z}{k}\Jacobiellcdk^{2}@{z}{k}}{1+k^{2}{k^{\prime}}^{2}\Jacobiellsdk^{4}@{z}{k}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiND(2*z, k) = ((JacobiND(z, k))^(2)+ (k)^(2)* (JacobiSD(z, k))^(2)* (JacobiCD(z, k))^(2))/(1 + (k)^(2)*1 - (k)^(2)*(JacobiSD(z, k))^(4))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiND[2*z, (k)^2] == Divide[(JacobiND[z, (k)^2])^(2)+ (k)^(2)* (JacobiSD[z, (k)^2])^(2)* (JacobiCD[z, (k)^2])^(2),1 + (k)^(2)*1 - (k)^(2)*(JacobiSD[z, (k)^2])^(4)]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.247856974+1.526848242*I
+| [https://dlmf.nist.gov/22.6.E10 22.6.E10] || <math qid="Q6944">\Jacobiellndk@{2z}{k} = \frac{\Jacobiellndk^{2}@{z}{k}+k^{2}\Jacobiellsdk^{2}@{z}{k}\Jacobiellcdk^{2}@{z}{k}}{1+k^{2}{k^{\prime}}^{2}\Jacobiellsdk^{4}@{z}{k}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellndk@{2z}{k} = \frac{\Jacobiellndk^{2}@{z}{k}+k^{2}\Jacobiellsdk^{2}@{z}{k}\Jacobiellcdk^{2}@{z}{k}}{1+k^{2}{k^{\prime}}^{2}\Jacobiellsdk^{4}@{z}{k}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiND(2*z, k) = ((JacobiND(z, k))^(2)+ (k)^(2)* (JacobiSD(z, k))^(2)* (JacobiCD(z, k))^(2))/(1 + (k)^(2)*1 - (k)^(2)*(JacobiSD(z, k))^(4))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiND[2*z, (k)^2] == Divide[(JacobiND[z, (k)^2])^(2)+ (k)^(2)* (JacobiSD[z, (k)^2])^(2)* (JacobiCD[z, (k)^2])^(2),1 + (k)^(2)*1 - (k)^(2)*(JacobiSD[z, (k)^2])^(4)]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.247856974+1.526848242*I
 Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.1237018962-.8644962079e-1*I
 Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.2478569728519586, 1.5268482411210251]
@@ Line 82: / Line 82: @@
 Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/22.6.E11 22.6.E11] || [[Item:Q6945|<math>\Jacobielldck@{2z}{k} = \frac{\Jacobielldck^{2}@{z}{k}+{k^{\prime}}^{2}\Jacobiellsck^{2}@{z}{k}\Jacobiellnck^{2}@{z}{k}}{1-{k^{\prime}}^{2}\Jacobiellsck^{4}@{z}{k}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobielldck@{2z}{k} = \frac{\Jacobielldck^{2}@{z}{k}+{k^{\prime}}^{2}\Jacobiellsck^{2}@{z}{k}\Jacobiellnck^{2}@{z}{k}}{1-{k^{\prime}}^{2}\Jacobiellsck^{4}@{z}{k}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiDC(2*z, k) = ((JacobiDC(z, k))^(2)+1 - (k)^(2)*(JacobiSC(z, k))^(2)* (JacobiNC(z, k))^(2))/(1 -1 - (k)^(2)*(JacobiSC(z, k))^(4))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiDC[2*z, (k)^2] == Divide[(JacobiDC[z, (k)^2])^(2)+1 - (k)^(2)*(JacobiSC[z, (k)^2])^(2)* (JacobiNC[z, (k)^2])^(2),1 -1 - (k)^(2)*(JacobiSC[z, (k)^2])^(4)]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.456738398+.1506627644*I
+| [https://dlmf.nist.gov/22.6.E11 22.6.E11] || <math qid="Q6945">\Jacobielldck@{2z}{k} = \frac{\Jacobielldck^{2}@{z}{k}+{k^{\prime}}^{2}\Jacobiellsck^{2}@{z}{k}\Jacobiellnck^{2}@{z}{k}}{1-{k^{\prime}}^{2}\Jacobiellsck^{4}@{z}{k}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobielldck@{2z}{k} = \frac{\Jacobielldck^{2}@{z}{k}+{k^{\prime}}^{2}\Jacobiellsck^{2}@{z}{k}\Jacobiellnck^{2}@{z}{k}}{1-{k^{\prime}}^{2}\Jacobiellsck^{4}@{z}{k}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiDC(2*z, k) = ((JacobiDC(z, k))^(2)+1 - (k)^(2)*(JacobiSC(z, k))^(2)* (JacobiNC(z, k))^(2))/(1 -1 - (k)^(2)*(JacobiSC(z, k))^(4))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiDC[2*z, (k)^2] == Divide[(JacobiDC[z, (k)^2])^(2)+1 - (k)^(2)*(JacobiSC[z, (k)^2])^(2)* (JacobiNC[z, (k)^2])^(2),1 -1 - (k)^(2)*(JacobiSC[z, (k)^2])^(4)]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.456738398+.1506627644*I
 Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -4.350355103-.3722352376e-1*I
 Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-1.456738400104645, 0.15066276425673586]
@@ Line 88: / Line 88: @@
 Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/22.6.E12 22.6.E12] || [[Item:Q6946|<math>\Jacobiellnck@{2z}{k} = \frac{\Jacobiellnck^{2}@{z}{k}+\Jacobiellsck^{2}@{z}{k}\Jacobielldck^{2}@{z}{k}}{1-{k^{\prime}}^{2}\Jacobiellsck^{4}@{z}{k}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellnck@{2z}{k} = \frac{\Jacobiellnck^{2}@{z}{k}+\Jacobiellsck^{2}@{z}{k}\Jacobielldck^{2}@{z}{k}}{1-{k^{\prime}}^{2}\Jacobiellsck^{4}@{z}{k}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiNC(2*z, k) = ((JacobiNC(z, k))^(2)+ (JacobiSC(z, k))^(2)* (JacobiDC(z, k))^(2))/(1 -1 - (k)^(2)*(JacobiSC(z, k))^(4))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiNC[2*z, (k)^2] == Divide[(JacobiNC[z, (k)^2])^(2)+ (JacobiSC[z, (k)^2])^(2)* (JacobiDC[z, (k)^2])^(2),1 -1 - (k)^(2)*(JacobiSC[z, (k)^2])^(4)]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.356171111+.335718656*I
+| [https://dlmf.nist.gov/22.6.E12 22.6.E12] || <math qid="Q6946">\Jacobiellnck@{2z}{k} = \frac{\Jacobiellnck^{2}@{z}{k}+\Jacobiellsck^{2}@{z}{k}\Jacobielldck^{2}@{z}{k}}{1-{k^{\prime}}^{2}\Jacobiellsck^{4}@{z}{k}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellnck@{2z}{k} = \frac{\Jacobiellnck^{2}@{z}{k}+\Jacobiellsck^{2}@{z}{k}\Jacobielldck^{2}@{z}{k}}{1-{k^{\prime}}^{2}\Jacobiellsck^{4}@{z}{k}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiNC(2*z, k) = ((JacobiNC(z, k))^(2)+ (JacobiSC(z, k))^(2)* (JacobiDC(z, k))^(2))/(1 -1 - (k)^(2)*(JacobiSC(z, k))^(4))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiNC[2*z, (k)^2] == Divide[(JacobiNC[z, (k)^2])^(2)+ (JacobiSC[z, (k)^2])^(2)* (JacobiDC[z, (k)^2])^(2),1 -1 - (k)^(2)*(JacobiSC[z, (k)^2])^(4)]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.356171111+.335718656*I
 Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .3210452605+.1984107752*I
 Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.356171110076661, 0.3357186535359711]
@@ Line 94: / Line 94: @@
 Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/22.6.E13 22.6.E13] || [[Item:Q6947|<math>\Jacobiellsck@{2z}{k} = \frac{2\Jacobiellsck@{z}{k}\Jacobielldck@{z}{k}\Jacobiellnck@{z}{k}}{1-{k^{\prime}}^{2}\Jacobiellsck^{4}@{z}{k}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellsck@{2z}{k} = \frac{2\Jacobiellsck@{z}{k}\Jacobielldck@{z}{k}\Jacobiellnck@{z}{k}}{1-{k^{\prime}}^{2}\Jacobiellsck^{4}@{z}{k}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiSC(2*z, k) = (2*JacobiSC(z, k)*JacobiDC(z, k)*JacobiNC(z, k))/(1 -1 - (k)^(2)*(JacobiSC(z, k))^(4))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiSC[2*z, (k)^2] == Divide[2*JacobiSC[z, (k)^2]*JacobiDC[z, (k)^2]*JacobiNC[z, (k)^2],1 -1 - (k)^(2)*(JacobiSC[z, (k)^2])^(4)]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.370082581+.423198902*I
+| [https://dlmf.nist.gov/22.6.E13 22.6.E13] || <math qid="Q6947">\Jacobiellsck@{2z}{k} = \frac{2\Jacobiellsck@{z}{k}\Jacobielldck@{z}{k}\Jacobiellnck@{z}{k}}{1-{k^{\prime}}^{2}\Jacobiellsck^{4}@{z}{k}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellsck@{2z}{k} = \frac{2\Jacobiellsck@{z}{k}\Jacobielldck@{z}{k}\Jacobiellnck@{z}{k}}{1-{k^{\prime}}^{2}\Jacobiellsck^{4}@{z}{k}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiSC(2*z, k) = (2*JacobiSC(z, k)*JacobiDC(z, k)*JacobiNC(z, k))/(1 -1 - (k)^(2)*(JacobiSC(z, k))^(4))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiSC[2*z, (k)^2] == Divide[2*JacobiSC[z, (k)^2]*JacobiDC[z, (k)^2]*JacobiNC[z, (k)^2],1 -1 - (k)^(2)*(JacobiSC[z, (k)^2])^(4)]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.370082581+.423198902*I
 Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .2742031773e-1-2.068263955*I
 Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.3700825790735573, 0.42319889849983916]
@@ Line 100: / Line 100: @@
 Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/22.6.E14 22.6.E14] || [[Item:Q6948|<math>\Jacobiellnsk@{2z}{k} = \frac{\Jacobiellnsk^{4}@{z}{k}-k^{2}}{2\Jacobiellcsk@{z}{k}\Jacobielldsk@{z}{k}\Jacobiellnsk@{z}{k}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellnsk@{2z}{k} = \frac{\Jacobiellnsk^{4}@{z}{k}-k^{2}}{2\Jacobiellcsk@{z}{k}\Jacobielldsk@{z}{k}\Jacobiellnsk@{z}{k}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiNS(2*z, k) = ((JacobiNS(z, k))^(4)- (k)^(2))/(2*JacobiCS(z, k)*JacobiDS(z, k)*JacobiNS(z, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiNS[2*z, (k)^2] == Divide[(JacobiNS[z, (k)^2])^(4)- (k)^(2),2*JacobiCS[z, (k)^2]*JacobiDS[z, (k)^2]*JacobiNS[z, (k)^2]]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 21] || Successful [Tested: 21]
+| [https://dlmf.nist.gov/22.6.E14 22.6.E14] || <math qid="Q6948">\Jacobiellnsk@{2z}{k} = \frac{\Jacobiellnsk^{4}@{z}{k}-k^{2}}{2\Jacobiellcsk@{z}{k}\Jacobielldsk@{z}{k}\Jacobiellnsk@{z}{k}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellnsk@{2z}{k} = \frac{\Jacobiellnsk^{4}@{z}{k}-k^{2}}{2\Jacobiellcsk@{z}{k}\Jacobielldsk@{z}{k}\Jacobiellnsk@{z}{k}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiNS(2*z, k) = ((JacobiNS(z, k))^(4)- (k)^(2))/(2*JacobiCS(z, k)*JacobiDS(z, k)*JacobiNS(z, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiNS[2*z, (k)^2] == Divide[(JacobiNS[z, (k)^2])^(4)- (k)^(2),2*JacobiCS[z, (k)^2]*JacobiDS[z, (k)^2]*JacobiNS[z, (k)^2]]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 21] || Successful [Tested: 21]
 |-
-| [https://dlmf.nist.gov/22.6.E15 22.6.E15] || [[Item:Q6949|<math>\Jacobielldsk@{2z}{k} = \frac{k^{2}{k^{\prime}}^{2}+\Jacobielldsk^{4}@{z}{k}}{2\Jacobiellcsk@{z}{k}\Jacobielldsk@{z}{k}\Jacobiellnsk@{z}{k}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobielldsk@{2z}{k} = \frac{k^{2}{k^{\prime}}^{2}+\Jacobielldsk^{4}@{z}{k}}{2\Jacobiellcsk@{z}{k}\Jacobielldsk@{z}{k}\Jacobiellnsk@{z}{k}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiDS(2*z, k) = ((k)^(2)*1 - (k)^(2)+ (JacobiDS(z, k))^(4))/(2*JacobiCS(z, k)*JacobiDS(z, k)*JacobiNS(z, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiDS[2*z, (k)^2] == Divide[(k)^(2)*1 - (k)^(2)+ (JacobiDS[z, (k)^2])^(4),2*JacobiCS[z, (k)^2]*JacobiDS[z, (k)^2]*JacobiNS[z, (k)^2]]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [14 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.1079800431-2.783083843*I
+| [https://dlmf.nist.gov/22.6.E15 22.6.E15] || <math qid="Q6949">\Jacobielldsk@{2z}{k} = \frac{k^{2}{k^{\prime}}^{2}+\Jacobielldsk^{4}@{z}{k}}{2\Jacobiellcsk@{z}{k}\Jacobielldsk@{z}{k}\Jacobiellnsk@{z}{k}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobielldsk@{2z}{k} = \frac{k^{2}{k^{\prime}}^{2}+\Jacobielldsk^{4}@{z}{k}}{2\Jacobiellcsk@{z}{k}\Jacobielldsk@{z}{k}\Jacobiellnsk@{z}{k}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiDS(2*z, k) = ((k)^(2)*1 - (k)^(2)+ (JacobiDS(z, k))^(4))/(2*JacobiCS(z, k)*JacobiDS(z, k)*JacobiNS(z, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiDS[2*z, (k)^2] == Divide[(k)^(2)*1 - (k)^(2)+ (JacobiDS[z, (k)^2])^(4),2*JacobiCS[z, (k)^2]*JacobiDS[z, (k)^2]*JacobiNS[z, (k)^2]]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [14 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.1079800431-2.783083843*I
 Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -6.118875072+.736498896*I
 Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 3}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [14 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.10798004208618706, -2.7830838428160787]
@@ Line 108: / Line 108: @@
 Test Values: {Rule[k, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/22.6.E16 22.6.E16] || [[Item:Q6950|<math>\Jacobiellcsk@{2z}{k} = \frac{\Jacobiellcsk^{4}@{z}{k}-{k^{\prime}}^{2}}{2\Jacobiellcsk@{z}{k}\Jacobielldsk@{z}{k}\Jacobiellnsk@{z}{k}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellcsk@{2z}{k} = \frac{\Jacobiellcsk^{4}@{z}{k}-{k^{\prime}}^{2}}{2\Jacobiellcsk@{z}{k}\Jacobielldsk@{z}{k}\Jacobiellnsk@{z}{k}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiCS(2*z, k) = ((JacobiCS(z, k))^(4)-1 - (k)^(2))/(2*JacobiCS(z, k)*JacobiDS(z, k)*JacobiNS(z, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiCS[2*z, (k)^2] == Divide[(JacobiCS[z, (k)^2])^(4)-1 - (k)^(2),2*JacobiCS[z, (k)^2]*JacobiDS[z, (k)^2]*JacobiNS[z, (k)^2]]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.528217681e-1+.9827060369*I
+| [https://dlmf.nist.gov/22.6.E16 22.6.E16] || <math qid="Q6950">\Jacobiellcsk@{2z}{k} = \frac{\Jacobiellcsk^{4}@{z}{k}-{k^{\prime}}^{2}}{2\Jacobiellcsk@{z}{k}\Jacobielldsk@{z}{k}\Jacobiellnsk@{z}{k}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellcsk@{2z}{k} = \frac{\Jacobiellcsk^{4}@{z}{k}-{k^{\prime}}^{2}}{2\Jacobiellcsk@{z}{k}\Jacobielldsk@{z}{k}\Jacobiellnsk@{z}{k}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>JacobiCS(2*z, k) = ((JacobiCS(z, k))^(4)-1 - (k)^(2))/(2*JacobiCS(z, k)*JacobiDS(z, k)*JacobiNS(z, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>JacobiCS[2*z, (k)^2] == Divide[(JacobiCS[z, (k)^2])^(4)-1 - (k)^(2),2*JacobiCS[z, (k)^2]*JacobiDS[z, (k)^2]*JacobiNS[z, (k)^2]]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.528217681e-1+.9827060369*I
 Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .7198669539e-1+1.855389227*I
 Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.05282176850410922, 0.9827060372847245]
@@ Line 114: / Line 114: @@
 Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/22.6.E17 22.6.E17] || [[Item:Q6951|<math>\frac{1-\Jacobiellcnk@{2z}{k}}{1+\Jacobiellcnk@{2z}{k}} = \frac{\Jacobiellsnk^{2}@{z}{k}\Jacobielldnk^{2}@{z}{k}}{\Jacobiellcnk^{2}@{z}{k}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{1-\Jacobiellcnk@{2z}{k}}{1+\Jacobiellcnk@{2z}{k}} = \frac{\Jacobiellsnk^{2}@{z}{k}\Jacobielldnk^{2}@{z}{k}}{\Jacobiellcnk^{2}@{z}{k}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(1 - JacobiCN(2*z, k))/(1 + JacobiCN(2*z, k)) = ((JacobiSN(z, k))^(2)* (JacobiDN(z, k))^(2))/((JacobiCN(z, k))^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1 - JacobiCN[2*z, (k)^2],1 + JacobiCN[2*z, (k)^2]] == Divide[(JacobiSN[z, (k)^2])^(2)* (JacobiDN[z, (k)^2])^(2),(JacobiCN[z, (k)^2])^(2)]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 21] || Successful [Tested: 21]
+| [https://dlmf.nist.gov/22.6.E17 22.6.E17] || <math qid="Q6951">\frac{1-\Jacobiellcnk@{2z}{k}}{1+\Jacobiellcnk@{2z}{k}} = \frac{\Jacobiellsnk^{2}@{z}{k}\Jacobielldnk^{2}@{z}{k}}{\Jacobiellcnk^{2}@{z}{k}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{1-\Jacobiellcnk@{2z}{k}}{1+\Jacobiellcnk@{2z}{k}} = \frac{\Jacobiellsnk^{2}@{z}{k}\Jacobielldnk^{2}@{z}{k}}{\Jacobiellcnk^{2}@{z}{k}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(1 - JacobiCN(2*z, k))/(1 + JacobiCN(2*z, k)) = ((JacobiSN(z, k))^(2)* (JacobiDN(z, k))^(2))/((JacobiCN(z, k))^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1 - JacobiCN[2*z, (k)^2],1 + JacobiCN[2*z, (k)^2]] == Divide[(JacobiSN[z, (k)^2])^(2)* (JacobiDN[z, (k)^2])^(2),(JacobiCN[z, (k)^2])^(2)]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 21] || Successful [Tested: 21]
 |-
-| [https://dlmf.nist.gov/22.6.E18 22.6.E18] || [[Item:Q6952|<math>\frac{1-\Jacobielldnk@{2z}{k}}{1+\Jacobielldnk@{2z}{k}} = \frac{k^{2}\Jacobiellsnk^{2}@{z}{k}\Jacobiellcnk^{2}@{z}{k}}{\Jacobielldnk^{2}@{z}{k}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{1-\Jacobielldnk@{2z}{k}}{1+\Jacobielldnk@{2z}{k}} = \frac{k^{2}\Jacobiellsnk^{2}@{z}{k}\Jacobiellcnk^{2}@{z}{k}}{\Jacobielldnk^{2}@{z}{k}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(1 - JacobiDN(2*z, k))/(1 + JacobiDN(2*z, k)) = ((k)^(2)* (JacobiSN(z, k))^(2)* (JacobiCN(z, k))^(2))/((JacobiDN(z, k))^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1 - JacobiDN[2*z, (k)^2],1 + JacobiDN[2*z, (k)^2]] == Divide[(k)^(2)* (JacobiSN[z, (k)^2])^(2)* (JacobiCN[z, (k)^2])^(2),(JacobiDN[z, (k)^2])^(2)]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 21] || Successful [Tested: 21]
+| [https://dlmf.nist.gov/22.6.E18 22.6.E18] || <math qid="Q6952">\frac{1-\Jacobielldnk@{2z}{k}}{1+\Jacobielldnk@{2z}{k}} = \frac{k^{2}\Jacobiellsnk^{2}@{z}{k}\Jacobiellcnk^{2}@{z}{k}}{\Jacobielldnk^{2}@{z}{k}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{1-\Jacobielldnk@{2z}{k}}{1+\Jacobielldnk@{2z}{k}} = \frac{k^{2}\Jacobiellsnk^{2}@{z}{k}\Jacobiellcnk^{2}@{z}{k}}{\Jacobielldnk^{2}@{z}{k}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(1 - JacobiDN(2*z, k))/(1 + JacobiDN(2*z, k)) = ((k)^(2)* (JacobiSN(z, k))^(2)* (JacobiCN(z, k))^(2))/((JacobiDN(z, k))^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1 - JacobiDN[2*z, (k)^2],1 + JacobiDN[2*z, (k)^2]] == Divide[(k)^(2)* (JacobiSN[z, (k)^2])^(2)* (JacobiCN[z, (k)^2])^(2),(JacobiDN[z, (k)^2])^(2)]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 21] || Successful [Tested: 21]
 |-
-| [https://dlmf.nist.gov/22.6.E19 22.6.E19] || [[Item:Q6953|<math>\Jacobiellsnk^{2}@{\tfrac{1}{2}z}{k} = \frac{1-\Jacobiellcnk@{z}{k}}{1+\Jacobielldnk@{z}{k}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellsnk^{2}@{\tfrac{1}{2}z}{k} = \frac{1-\Jacobiellcnk@{z}{k}}{1+\Jacobielldnk@{z}{k}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(JacobiSN((1)/(2)*z, k))^(2) = (1 - JacobiCN(z, k))/(1 + JacobiDN(z, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(JacobiSN[Divide[1,2]*z, (k)^2])^(2) == Divide[1 - JacobiCN[z, (k)^2],1 + JacobiDN[z, (k)^2]]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 21] || Successful [Tested: 21]
+| [https://dlmf.nist.gov/22.6.E19 22.6.E19] || <math qid="Q6953">\Jacobiellsnk^{2}@{\tfrac{1}{2}z}{k} = \frac{1-\Jacobiellcnk@{z}{k}}{1+\Jacobielldnk@{z}{k}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellsnk^{2}@{\tfrac{1}{2}z}{k} = \frac{1-\Jacobiellcnk@{z}{k}}{1+\Jacobielldnk@{z}{k}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(JacobiSN((1)/(2)*z, k))^(2) = (1 - JacobiCN(z, k))/(1 + JacobiDN(z, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(JacobiSN[Divide[1,2]*z, (k)^2])^(2) == Divide[1 - JacobiCN[z, (k)^2],1 + JacobiDN[z, (k)^2]]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 21] || Successful [Tested: 21]
 |-
-| [https://dlmf.nist.gov/22.6.E19 22.6.E19] || [[Item:Q6953|<math>\frac{1-\Jacobiellcnk@{z}{k}}{1+\Jacobielldnk@{z}{k}} = \frac{1-\Jacobielldnk@{z}{k}}{k^{2}(1+\Jacobiellcnk@{z}{k})}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{1-\Jacobiellcnk@{z}{k}}{1+\Jacobielldnk@{z}{k}} = \frac{1-\Jacobielldnk@{z}{k}}{k^{2}(1+\Jacobiellcnk@{z}{k})}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(1 - JacobiCN(z, k))/(1 + JacobiDN(z, k)) = (1 - JacobiDN(z, k))/((k)^(2)*(1 + JacobiCN(z, k)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1 - JacobiCN[z, (k)^2],1 + JacobiDN[z, (k)^2]] == Divide[1 - JacobiDN[z, (k)^2],(k)^(2)*(1 + JacobiCN[z, (k)^2])]</syntaxhighlight> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 21]
+| [https://dlmf.nist.gov/22.6.E19 22.6.E19] || <math qid="Q6953">\frac{1-\Jacobiellcnk@{z}{k}}{1+\Jacobielldnk@{z}{k}} = \frac{1-\Jacobielldnk@{z}{k}}{k^{2}(1+\Jacobiellcnk@{z}{k})}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{1-\Jacobiellcnk@{z}{k}}{1+\Jacobielldnk@{z}{k}} = \frac{1-\Jacobielldnk@{z}{k}}{k^{2}(1+\Jacobiellcnk@{z}{k})}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(1 - JacobiCN(z, k))/(1 + JacobiDN(z, k)) = (1 - JacobiDN(z, k))/((k)^(2)*(1 + JacobiCN(z, k)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1 - JacobiCN[z, (k)^2],1 + JacobiDN[z, (k)^2]] == Divide[1 - JacobiDN[z, (k)^2],(k)^(2)*(1 + JacobiCN[z, (k)^2])]</syntaxhighlight> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 21]
 |-
-| [https://dlmf.nist.gov/22.6.E19 22.6.E19] || [[Item:Q6953|<math>\frac{1-\Jacobielldnk@{z}{k}}{k^{2}(1+\Jacobiellcnk@{z}{k})} = \frac{\Jacobielldnk@{z}{k}-k^{2}\Jacobiellcnk@{z}{k}-{k^{\prime}}^{2}}{k^{2}(\Jacobielldnk@{z}{k}-\Jacobiellcnk@{z}{k})}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{1-\Jacobielldnk@{z}{k}}{k^{2}(1+\Jacobiellcnk@{z}{k})} = \frac{\Jacobielldnk@{z}{k}-k^{2}\Jacobiellcnk@{z}{k}-{k^{\prime}}^{2}}{k^{2}(\Jacobielldnk@{z}{k}-\Jacobiellcnk@{z}{k})}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(1 - JacobiDN(z, k))/((k)^(2)*(1 + JacobiCN(z, k))) = (JacobiDN(z, k)- (k)^(2)* JacobiCN(z, k)-1 - (k)^(2))/((k)^(2)*(JacobiDN(z, k)- JacobiCN(z, k)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1 - JacobiDN[z, (k)^2],(k)^(2)*(1 + JacobiCN[z, (k)^2])] == Divide[JacobiDN[z, (k)^2]- (k)^(2)* JacobiCN[z, (k)^2]-1 - (k)^(2),(k)^(2)*(JacobiDN[z, (k)^2]- JacobiCN[z, (k)^2])]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Float(infinity)+.1810063706*I
+| [https://dlmf.nist.gov/22.6.E19 22.6.E19] || <math qid="Q6953">\frac{1-\Jacobielldnk@{z}{k}}{k^{2}(1+\Jacobiellcnk@{z}{k})} = \frac{\Jacobielldnk@{z}{k}-k^{2}\Jacobiellcnk@{z}{k}-{k^{\prime}}^{2}}{k^{2}(\Jacobielldnk@{z}{k}-\Jacobiellcnk@{z}{k})}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{1-\Jacobielldnk@{z}{k}}{k^{2}(1+\Jacobiellcnk@{z}{k})} = \frac{\Jacobielldnk@{z}{k}-k^{2}\Jacobiellcnk@{z}{k}-{k^{\prime}}^{2}}{k^{2}(\Jacobielldnk@{z}{k}-\Jacobiellcnk@{z}{k})}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(1 - JacobiDN(z, k))/((k)^(2)*(1 + JacobiCN(z, k))) = (JacobiDN(z, k)- (k)^(2)* JacobiCN(z, k)-1 - (k)^(2))/((k)^(2)*(JacobiDN(z, k)- JacobiCN(z, k)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1 - JacobiDN[z, (k)^2],(k)^(2)*(1 + JacobiCN[z, (k)^2])] == Divide[JacobiDN[z, (k)^2]- (k)^(2)* JacobiCN[z, (k)^2]-1 - (k)^(2),(k)^(2)*(JacobiDN[z, (k)^2]- JacobiCN[z, (k)^2])]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Float(infinity)+.1810063706*I
 Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.050510101+1.261106800*I
 Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: DirectedInfinity[]
@@ Line 128: / Line 128: @@
 Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/22.6.E20 22.6.E20] || [[Item:Q6954|<math>\Jacobiellcnk^{2}@{\tfrac{1}{2}z}{k} = \frac{-{k^{\prime}}^{2}+\Jacobielldnk@{z}{k}+k^{2}\Jacobiellcnk@{z}{k}}{k^{2}(1+\Jacobiellcnk@{z}{k})}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellcnk^{2}@{\tfrac{1}{2}z}{k} = \frac{-{k^{\prime}}^{2}+\Jacobielldnk@{z}{k}+k^{2}\Jacobiellcnk@{z}{k}}{k^{2}(1+\Jacobiellcnk@{z}{k})}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(JacobiCN((1)/(2)*z, k))^(2) = (-1 - (k)^(2)+ JacobiDN(z, k)+ (k)^(2)* JacobiCN(z, k))/((k)^(2)*(1 + JacobiCN(z, k)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(JacobiCN[Divide[1,2]*z, (k)^2])^(2) == Divide[-1 - (k)^(2)+ JacobiDN[z, (k)^2]+ (k)^(2)* JacobiCN[z, (k)^2],(k)^(2)*(1 + JacobiCN[z, (k)^2])]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.140351911+.1810063706*I
+| [https://dlmf.nist.gov/22.6.E20 22.6.E20] || <math qid="Q6954">\Jacobiellcnk^{2}@{\tfrac{1}{2}z}{k} = \frac{-{k^{\prime}}^{2}+\Jacobielldnk@{z}{k}+k^{2}\Jacobiellcnk@{z}{k}}{k^{2}(1+\Jacobiellcnk@{z}{k})}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobiellcnk^{2}@{\tfrac{1}{2}z}{k} = \frac{-{k^{\prime}}^{2}+\Jacobielldnk@{z}{k}+k^{2}\Jacobiellcnk@{z}{k}}{k^{2}(1+\Jacobiellcnk@{z}{k})}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(JacobiCN((1)/(2)*z, k))^(2) = (-1 - (k)^(2)+ JacobiDN(z, k)+ (k)^(2)* JacobiCN(z, k))/((k)^(2)*(1 + JacobiCN(z, k)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(JacobiCN[Divide[1,2]*z, (k)^2])^(2) == Divide[-1 - (k)^(2)+ JacobiDN[z, (k)^2]+ (k)^(2)* JacobiCN[z, (k)^2],(k)^(2)*(1 + JacobiCN[z, (k)^2])]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.140351911+.1810063706*I
 Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.153509822-.96502865e-2*I
 Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.140351911309134, 0.18100637055769858]
@@ Line 134: / Line 134: @@
 Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/22.6.E20 22.6.E20] || [[Item:Q6954|<math>\frac{-{k^{\prime}}^{2}+\Jacobielldnk@{z}{k}+k^{2}\Jacobiellcnk@{z}{k}}{k^{2}(1+\Jacobiellcnk@{z}{k})} = \frac{{k^{\prime}}^{2}(1-\Jacobielldnk@{z}{k})}{k^{2}(\Jacobielldnk@{z}{k}-\Jacobiellcnk@{z}{k})}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{-{k^{\prime}}^{2}+\Jacobielldnk@{z}{k}+k^{2}\Jacobiellcnk@{z}{k}}{k^{2}(1+\Jacobiellcnk@{z}{k})} = \frac{{k^{\prime}}^{2}(1-\Jacobielldnk@{z}{k})}{k^{2}(\Jacobielldnk@{z}{k}-\Jacobiellcnk@{z}{k})}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(-1 - (k)^(2)+ JacobiDN(z, k)+ (k)^(2)* JacobiCN(z, k))/((k)^(2)*(1 + JacobiCN(z, k))) = (1 - (k)^(2)*(1 - JacobiDN(z, k)))/((k)^(2)*(JacobiDN(z, k)- JacobiCN(z, k)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[-1 - (k)^(2)+ JacobiDN[z, (k)^2]+ (k)^(2)* JacobiCN[z, (k)^2],(k)^(2)*(1 + JacobiCN[z, (k)^2])] == Divide[1 - (k)^(2)*(1 - JacobiDN[z, (k)^2]),(k)^(2)*(JacobiDN[z, (k)^2]- JacobiCN[z, (k)^2])]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Float(infinity)+Float(infinity)*I
+| [https://dlmf.nist.gov/22.6.E20 22.6.E20] || <math qid="Q6954">\frac{-{k^{\prime}}^{2}+\Jacobielldnk@{z}{k}+k^{2}\Jacobiellcnk@{z}{k}}{k^{2}(1+\Jacobiellcnk@{z}{k})} = \frac{{k^{\prime}}^{2}(1-\Jacobielldnk@{z}{k})}{k^{2}(\Jacobielldnk@{z}{k}-\Jacobiellcnk@{z}{k})}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{-{k^{\prime}}^{2}+\Jacobielldnk@{z}{k}+k^{2}\Jacobiellcnk@{z}{k}}{k^{2}(1+\Jacobiellcnk@{z}{k})} = \frac{{k^{\prime}}^{2}(1-\Jacobielldnk@{z}{k})}{k^{2}(\Jacobielldnk@{z}{k}-\Jacobiellcnk@{z}{k})}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(-1 - (k)^(2)+ JacobiDN(z, k)+ (k)^(2)* JacobiCN(z, k))/((k)^(2)*(1 + JacobiCN(z, k))) = (1 - (k)^(2)*(1 - JacobiDN(z, k)))/((k)^(2)*(JacobiDN(z, k)- JacobiCN(z, k)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[-1 - (k)^(2)+ JacobiDN[z, (k)^2]+ (k)^(2)* JacobiCN[z, (k)^2],(k)^(2)*(1 + JacobiCN[z, (k)^2])] == Divide[1 - (k)^(2)*(1 - JacobiDN[z, (k)^2]),(k)^(2)*(JacobiDN[z, (k)^2]- JacobiCN[z, (k)^2])]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Float(infinity)+Float(infinity)*I
 Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.304876195-.1041070951*I
 Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: DirectedInfinity[]
@@ Line 140: / Line 140: @@
 Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/22.6.E20 22.6.E20] || [[Item:Q6954|<math>\frac{{k^{\prime}}^{2}(1-\Jacobielldnk@{z}{k})}{k^{2}(\Jacobielldnk@{z}{k}-\Jacobiellcnk@{z}{k})} = \frac{{k^{\prime}}^{2}(1+\Jacobiellcnk@{z}{k})}{{k^{\prime}}^{2}+\Jacobielldnk@{z}{k}-k^{2}\Jacobiellcnk@{z}{k}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{{k^{\prime}}^{2}(1-\Jacobielldnk@{z}{k})}{k^{2}(\Jacobielldnk@{z}{k}-\Jacobiellcnk@{z}{k})} = \frac{{k^{\prime}}^{2}(1+\Jacobiellcnk@{z}{k})}{{k^{\prime}}^{2}+\Jacobielldnk@{z}{k}-k^{2}\Jacobiellcnk@{z}{k}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(1 - (k)^(2)*(1 - JacobiDN(z, k)))/((k)^(2)*(JacobiDN(z, k)- JacobiCN(z, k))) = (1 - (k)^(2)*(1 + JacobiCN(z, k)))/(1 - (k)^(2)+ JacobiDN(z, k)- (k)^(2)* JacobiCN(z, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1 - (k)^(2)*(1 - JacobiDN[z, (k)^2]),(k)^(2)*(JacobiDN[z, (k)^2]- JacobiCN[z, (k)^2])] == Divide[1 - (k)^(2)*(1 + JacobiCN[z, (k)^2]),1 - (k)^(2)+ JacobiDN[z, (k)^2]- (k)^(2)* JacobiCN[z, (k)^2]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Float(infinity)-Float(infinity)*I
+| [https://dlmf.nist.gov/22.6.E20 22.6.E20] || <math qid="Q6954">\frac{{k^{\prime}}^{2}(1-\Jacobielldnk@{z}{k})}{k^{2}(\Jacobielldnk@{z}{k}-\Jacobiellcnk@{z}{k})} = \frac{{k^{\prime}}^{2}(1+\Jacobiellcnk@{z}{k})}{{k^{\prime}}^{2}+\Jacobielldnk@{z}{k}-k^{2}\Jacobiellcnk@{z}{k}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{{k^{\prime}}^{2}(1-\Jacobielldnk@{z}{k})}{k^{2}(\Jacobielldnk@{z}{k}-\Jacobiellcnk@{z}{k})} = \frac{{k^{\prime}}^{2}(1+\Jacobiellcnk@{z}{k})}{{k^{\prime}}^{2}+\Jacobielldnk@{z}{k}-k^{2}\Jacobiellcnk@{z}{k}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(1 - (k)^(2)*(1 - JacobiDN(z, k)))/((k)^(2)*(JacobiDN(z, k)- JacobiCN(z, k))) = (1 - (k)^(2)*(1 + JacobiCN(z, k)))/(1 - (k)^(2)+ JacobiDN(z, k)- (k)^(2)* JacobiCN(z, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1 - (k)^(2)*(1 - JacobiDN[z, (k)^2]),(k)^(2)*(JacobiDN[z, (k)^2]- JacobiCN[z, (k)^2])] == Divide[1 - (k)^(2)*(1 + JacobiCN[z, (k)^2]),1 - (k)^(2)+ JacobiDN[z, (k)^2]- (k)^(2)* JacobiCN[z, (k)^2]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Float(infinity)-Float(infinity)*I
 Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .315116621e-1+.1309658139*I
 Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
@@ Line 146: / Line 146: @@
 Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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-| [https://dlmf.nist.gov/22.6.E21 22.6.E21] || [[Item:Q6955|<math>\Jacobielldnk^{2}@{\tfrac{1}{2}z}{k} = \frac{k^{2}\Jacobiellcnk@{z}{k}+\Jacobielldnk@{z}{k}+{k^{\prime}}^{2}}{1+\Jacobielldnk@{z}{k}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobielldnk^{2}@{\tfrac{1}{2}z}{k} = \frac{k^{2}\Jacobiellcnk@{z}{k}+\Jacobielldnk@{z}{k}+{k^{\prime}}^{2}}{1+\Jacobielldnk@{z}{k}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(JacobiDN((1)/(2)*z, k))^(2) = ((k)^(2)* JacobiCN(z, k)+ JacobiDN(z, k)+1 - (k)^(2))/(1 + JacobiDN(z, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(JacobiDN[Divide[1,2]*z, (k)^2])^(2) == Divide[(k)^(2)* JacobiCN[z, (k)^2]+ JacobiDN[z, (k)^2]+1 - (k)^(2),1 + JacobiDN[z, (k)^2]]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 21] || Successful [Tested: 21]
+| [https://dlmf.nist.gov/22.6.E21 22.6.E21] || <math qid="Q6955">\Jacobielldnk^{2}@{\tfrac{1}{2}z}{k} = \frac{k^{2}\Jacobiellcnk@{z}{k}+\Jacobielldnk@{z}{k}+{k^{\prime}}^{2}}{1+\Jacobielldnk@{z}{k}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Jacobielldnk^{2}@{\tfrac{1}{2}z}{k} = \frac{k^{2}\Jacobiellcnk@{z}{k}+\Jacobielldnk@{z}{k}+{k^{\prime}}^{2}}{1+\Jacobielldnk@{z}{k}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(JacobiDN((1)/(2)*z, k))^(2) = ((k)^(2)* JacobiCN(z, k)+ JacobiDN(z, k)+1 - (k)^(2))/(1 + JacobiDN(z, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(JacobiDN[Divide[1,2]*z, (k)^2])^(2) == Divide[(k)^(2)* JacobiCN[z, (k)^2]+ JacobiDN[z, (k)^2]+1 - (k)^(2),1 + JacobiDN[z, (k)^2]]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 21] || Successful [Tested: 21]
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-| [https://dlmf.nist.gov/22.6.E21 22.6.E21] || [[Item:Q6955|<math>\frac{k^{2}\Jacobiellcnk@{z}{k}+\Jacobielldnk@{z}{k}+{k^{\prime}}^{2}}{1+\Jacobielldnk@{z}{k}} = \frac{{k^{\prime}}^{2}(1-\Jacobiellcnk@{z}{k})}{\Jacobielldnk@{z}{k}-\Jacobiellcnk@{z}{k}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{k^{2}\Jacobiellcnk@{z}{k}+\Jacobielldnk@{z}{k}+{k^{\prime}}^{2}}{1+\Jacobielldnk@{z}{k}} = \frac{{k^{\prime}}^{2}(1-\Jacobiellcnk@{z}{k})}{\Jacobielldnk@{z}{k}-\Jacobiellcnk@{z}{k}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>((k)^(2)* JacobiCN(z, k)+ JacobiDN(z, k)+1 - (k)^(2))/(1 + JacobiDN(z, k)) = (1 - (k)^(2)*(1 - JacobiCN(z, k)))/(JacobiDN(z, k)- JacobiCN(z, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[(k)^(2)* JacobiCN[z, (k)^2]+ JacobiDN[z, (k)^2]+1 - (k)^(2),1 + JacobiDN[z, (k)^2]] == Divide[1 - (k)^(2)*(1 - JacobiCN[z, (k)^2]),JacobiDN[z, (k)^2]- JacobiCN[z, (k)^2]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Float(infinity)+Float(infinity)*I
+| [https://dlmf.nist.gov/22.6.E21 22.6.E21] || <math qid="Q6955">\frac{k^{2}\Jacobiellcnk@{z}{k}+\Jacobielldnk@{z}{k}+{k^{\prime}}^{2}}{1+\Jacobielldnk@{z}{k}} = \frac{{k^{\prime}}^{2}(1-\Jacobiellcnk@{z}{k})}{\Jacobielldnk@{z}{k}-\Jacobiellcnk@{z}{k}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{k^{2}\Jacobiellcnk@{z}{k}+\Jacobielldnk@{z}{k}+{k^{\prime}}^{2}}{1+\Jacobielldnk@{z}{k}} = \frac{{k^{\prime}}^{2}(1-\Jacobiellcnk@{z}{k})}{\Jacobielldnk@{z}{k}-\Jacobiellcnk@{z}{k}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>((k)^(2)* JacobiCN(z, k)+ JacobiDN(z, k)+1 - (k)^(2))/(1 + JacobiDN(z, k)) = (1 - (k)^(2)*(1 - JacobiCN(z, k)))/(JacobiDN(z, k)- JacobiCN(z, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[(k)^(2)* JacobiCN[z, (k)^2]+ JacobiDN[z, (k)^2]+1 - (k)^(2),1 + JacobiDN[z, (k)^2]] == Divide[1 - (k)^(2)*(1 - JacobiCN[z, (k)^2]),JacobiDN[z, (k)^2]- JacobiCN[z, (k)^2]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Float(infinity)+Float(infinity)*I
 Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .3945345066-.4550295262*I
 Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: DirectedInfinity[]
@@ Line 154: / Line 154: @@
 Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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-| [https://dlmf.nist.gov/22.6.E21 22.6.E21] || [[Item:Q6955|<math>\frac{{k^{\prime}}^{2}(1-\Jacobiellcnk@{z}{k})}{\Jacobielldnk@{z}{k}-\Jacobiellcnk@{z}{k}} = \frac{{k^{\prime}}^{2}(1+\Jacobielldnk@{z}{k})}{{k^{\prime}}^{2}+\Jacobielldnk@{z}{k}-k^{2}\Jacobiellcnk@{z}{k}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{{k^{\prime}}^{2}(1-\Jacobiellcnk@{z}{k})}{\Jacobielldnk@{z}{k}-\Jacobiellcnk@{z}{k}} = \frac{{k^{\prime}}^{2}(1+\Jacobielldnk@{z}{k})}{{k^{\prime}}^{2}+\Jacobielldnk@{z}{k}-k^{2}\Jacobiellcnk@{z}{k}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(1 - (k)^(2)*(1 - JacobiCN(z, k)))/(JacobiDN(z, k)- JacobiCN(z, k)) = (1 - (k)^(2)*(1 + JacobiDN(z, k)))/(1 - (k)^(2)+ JacobiDN(z, k)- (k)^(2)* JacobiCN(z, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1 - (k)^(2)*(1 - JacobiCN[z, (k)^2]),JacobiDN[z, (k)^2]- JacobiCN[z, (k)^2]] == Divide[1 - (k)^(2)*(1 + JacobiDN[z, (k)^2]),1 - (k)^(2)+ JacobiDN[z, (k)^2]- (k)^(2)* JacobiCN[z, (k)^2]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Float(infinity)-Float(infinity)*I
+| [https://dlmf.nist.gov/22.6.E21 22.6.E21] || <math qid="Q6955">\frac{{k^{\prime}}^{2}(1-\Jacobiellcnk@{z}{k})}{\Jacobielldnk@{z}{k}-\Jacobiellcnk@{z}{k}} = \frac{{k^{\prime}}^{2}(1+\Jacobielldnk@{z}{k})}{{k^{\prime}}^{2}+\Jacobielldnk@{z}{k}-k^{2}\Jacobiellcnk@{z}{k}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{{k^{\prime}}^{2}(1-\Jacobiellcnk@{z}{k})}{\Jacobielldnk@{z}{k}-\Jacobiellcnk@{z}{k}} = \frac{{k^{\prime}}^{2}(1+\Jacobielldnk@{z}{k})}{{k^{\prime}}^{2}+\Jacobielldnk@{z}{k}-k^{2}\Jacobiellcnk@{z}{k}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(1 - (k)^(2)*(1 - JacobiCN(z, k)))/(JacobiDN(z, k)- JacobiCN(z, k)) = (1 - (k)^(2)*(1 + JacobiDN(z, k)))/(1 - (k)^(2)+ JacobiDN(z, k)- (k)^(2)* JacobiCN(z, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1 - (k)^(2)*(1 - JacobiCN[z, (k)^2]),JacobiDN[z, (k)^2]- JacobiCN[z, (k)^2]] == Divide[1 - (k)^(2)*(1 + JacobiDN[z, (k)^2]),1 - (k)^(2)+ JacobiDN[z, (k)^2]- (k)^(2)* JacobiCN[z, (k)^2]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Float(infinity)-Float(infinity)*I
 Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.3624296261+.6038808640*I
 Test Values: {z = 1/2*3^(1/2)+1/2*I, k = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
@@ Line 160: / Line 160: @@
 Test Values: {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/22.6.E22 22.6.E22] || [[Item:Q6956|<math>\genJacobiellk{p}{q}^{2}@{\tfrac{1}{2}z}{k} = \frac{\genJacobiellk{p}{s}@{z}{k}+\genJacobiellk{r}{s}@{z}{k}}{\genJacobiellk{q}{s}@{z}{k}+\genJacobiellk{r}{s}@{z}{k}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\genJacobiellk{p}{q}^{2}@{\tfrac{1}{2}z}{k} = \frac{\genJacobiellk{p}{s}@{z}{k}+\genJacobiellk{r}{s}@{z}{k}}{\genJacobiellk{q}{s}@{z}{k}+\genJacobiellk{r}{s}@{z}{k}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>genJacobiellk(p)*(q)^(2)* (1)/(2)*zk = (genJacobiellk(p)*s* z*k + genJacobiellk(r)*s* z*k)/(genJacobiellk(q)*s* z*k + genJacobiellk(r)*s* z*k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>genJacobiellk[p]*(q)^(2)* Divide[1,2]*zk == Divide[genJacobiellk[p]*s* z*k + genJacobiellk[r]*s* z*k,genJacobiellk[q]*s* z*k + genJacobiellk[r]*s* z*k]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Complex[-0.9999999999999999, -2.7755575615628914*^-17], Times[Complex[0.0, 0.5], genJacobiellk, zk]]
+| [https://dlmf.nist.gov/22.6.E22 22.6.E22] || <math qid="Q6956">\genJacobiellk{p}{q}^{2}@{\tfrac{1}{2}z}{k} = \frac{\genJacobiellk{p}{s}@{z}{k}+\genJacobiellk{r}{s}@{z}{k}}{\genJacobiellk{q}{s}@{z}{k}+\genJacobiellk{r}{s}@{z}{k}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\genJacobiellk{p}{q}^{2}@{\tfrac{1}{2}z}{k} = \frac{\genJacobiellk{p}{s}@{z}{k}+\genJacobiellk{r}{s}@{z}{k}}{\genJacobiellk{q}{s}@{z}{k}+\genJacobiellk{r}{s}@{z}{k}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>genJacobiellk(p)*(q)^(2)* (1)/(2)*zk = (genJacobiellk(p)*s* z*k + genJacobiellk(r)*s* z*k)/(genJacobiellk(q)*s* z*k + genJacobiellk(r)*s* z*k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>genJacobiellk[p]*(q)^(2)* Divide[1,2]*zk == Divide[genJacobiellk[p]*s* z*k + genJacobiellk[r]*s* z*k,genJacobiellk[q]*s* z*k + genJacobiellk[r]*s* z*k]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Complex[-0.9999999999999999, -2.7755575615628914*^-17], Times[Complex[0.0, 0.5], genJacobiellk, zk]]
 Test Values: {Rule[k, 1], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[r, -1.5], Rule[s, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[-0.9999999999999999, -2.7755575615628914*^-17], Times[Complex[0.0, 0.5], genJacobiellk, zk]]
 Test Values: {Rule[k, 2], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[r, -1.5], Rule[s, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/22.6.E22 22.6.E22] || [[Item:Q6956|<math>\frac{\genJacobiellk{p}{s}@{z}{k}+\genJacobiellk{r}{s}@{z}{k}}{\genJacobiellk{q}{s}@{z}{k}+\genJacobiellk{r}{s}@{z}{k}} = \frac{\genJacobiellk{p}{q}@{z}{k}+\genJacobiellk{r}{q}@{z}{k}}{1+\genJacobiellk{r}{q}@{z}{k}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{\genJacobiellk{p}{s}@{z}{k}+\genJacobiellk{r}{s}@{z}{k}}{\genJacobiellk{q}{s}@{z}{k}+\genJacobiellk{r}{s}@{z}{k}} = \frac{\genJacobiellk{p}{q}@{z}{k}+\genJacobiellk{r}{q}@{z}{k}}{1+\genJacobiellk{r}{q}@{z}{k}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(genJacobiellk(p)*s* z*k + genJacobiellk(r)*s* z*k)/(genJacobiellk(q)*s* z*k + genJacobiellk(r)*s* z*k) = (genJacobiellk(p)*q* z*k + genJacobiellk(r)*q* z*k)/(1 + genJacobiellk(r)*q* z*k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[genJacobiellk[p]*s* z*k + genJacobiellk[r]*s* z*k,genJacobiellk[q]*s* z*k + genJacobiellk[r]*s* z*k] == Divide[genJacobiellk[p]*q* z*k + genJacobiellk[r]*q* z*k,1 + genJacobiellk[r]*q* z*k]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.9999999999999999, 2.7755575615628914*^-17], Times[Complex[0.7500000000000001, 0.2990381056766578], Power[Plus[1.0, Times[Complex[-0.7500000000000001, -1.2990381056766578], genJacobiellk]], -1], genJacobiellk]]
+| [https://dlmf.nist.gov/22.6.E22 22.6.E22] || <math qid="Q6956">\frac{\genJacobiellk{p}{s}@{z}{k}+\genJacobiellk{r}{s}@{z}{k}}{\genJacobiellk{q}{s}@{z}{k}+\genJacobiellk{r}{s}@{z}{k}} = \frac{\genJacobiellk{p}{q}@{z}{k}+\genJacobiellk{r}{q}@{z}{k}}{1+\genJacobiellk{r}{q}@{z}{k}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{\genJacobiellk{p}{s}@{z}{k}+\genJacobiellk{r}{s}@{z}{k}}{\genJacobiellk{q}{s}@{z}{k}+\genJacobiellk{r}{s}@{z}{k}} = \frac{\genJacobiellk{p}{q}@{z}{k}+\genJacobiellk{r}{q}@{z}{k}}{1+\genJacobiellk{r}{q}@{z}{k}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(genJacobiellk(p)*s* z*k + genJacobiellk(r)*s* z*k)/(genJacobiellk(q)*s* z*k + genJacobiellk(r)*s* z*k) = (genJacobiellk(p)*q* z*k + genJacobiellk(r)*q* z*k)/(1 + genJacobiellk(r)*q* z*k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[genJacobiellk[p]*s* z*k + genJacobiellk[r]*s* z*k,genJacobiellk[q]*s* z*k + genJacobiellk[r]*s* z*k] == Divide[genJacobiellk[p]*q* z*k + genJacobiellk[r]*q* z*k,1 + genJacobiellk[r]*q* z*k]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.9999999999999999, 2.7755575615628914*^-17], Times[Complex[0.7500000000000001, 0.2990381056766578], Power[Plus[1.0, Times[Complex[-0.7500000000000001, -1.2990381056766578], genJacobiellk]], -1], genJacobiellk]]
 Test Values: {Rule[k, 1], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[r, -1.5], Rule[s, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.9999999999999999, 2.7755575615628914*^-17], Times[Complex[1.5000000000000002, 0.5980762113533156], Power[Plus[1.0, Times[Complex[-1.5000000000000002, -2.5980762113533156], genJacobiellk]], -1], genJacobiellk]]
 Test Values: {Rule[k, 2], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[r, -1.5], Rule[s, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/22.6.E22 22.6.E22] || [[Item:Q6956|<math>\frac{\genJacobiellk{p}{q}@{z}{k}+\genJacobiellk{r}{q}@{z}{k}}{1+\genJacobiellk{r}{q}@{z}{k}} = \frac{\genJacobiellk{p}{r}@{z}{k}+1}{\genJacobiellk{q}{r}@{z}{k}+1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{\genJacobiellk{p}{q}@{z}{k}+\genJacobiellk{r}{q}@{z}{k}}{1+\genJacobiellk{r}{q}@{z}{k}} = \frac{\genJacobiellk{p}{r}@{z}{k}+1}{\genJacobiellk{q}{r}@{z}{k}+1}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(genJacobiellk(p)*q* z*k + genJacobiellk(r)*q* z*k)/(1 + genJacobiellk(r)*q* z*k) = (genJacobiellk(p)*r* z*k + 1)/(genJacobiellk(q)*r* z*k + 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[genJacobiellk[p]*q* z*k + genJacobiellk[r]*q* z*k,1 + genJacobiellk[r]*q* z*k] == Divide[genJacobiellk[p]*r* z*k + 1,genJacobiellk[q]*r* z*k + 1]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[-1.0, Times[Complex[-0.7500000000000001, -0.2990381056766578], Power[Plus[1.0, Times[Complex[-0.7500000000000001, -1.2990381056766578], genJacobiellk]], -1], genJacobiellk]]
+| [https://dlmf.nist.gov/22.6.E22 22.6.E22] || <math qid="Q6956">\frac{\genJacobiellk{p}{q}@{z}{k}+\genJacobiellk{r}{q}@{z}{k}}{1+\genJacobiellk{r}{q}@{z}{k}} = \frac{\genJacobiellk{p}{r}@{z}{k}+1}{\genJacobiellk{q}{r}@{z}{k}+1}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{\genJacobiellk{p}{q}@{z}{k}+\genJacobiellk{r}{q}@{z}{k}}{1+\genJacobiellk{r}{q}@{z}{k}} = \frac{\genJacobiellk{p}{r}@{z}{k}+1}{\genJacobiellk{q}{r}@{z}{k}+1}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(genJacobiellk(p)*q* z*k + genJacobiellk(r)*q* z*k)/(1 + genJacobiellk(r)*q* z*k) = (genJacobiellk(p)*r* z*k + 1)/(genJacobiellk(q)*r* z*k + 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[genJacobiellk[p]*q* z*k + genJacobiellk[r]*q* z*k,1 + genJacobiellk[r]*q* z*k] == Divide[genJacobiellk[p]*r* z*k + 1,genJacobiellk[q]*r* z*k + 1]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[-1.0, Times[Complex[-0.7500000000000001, -0.2990381056766578], Power[Plus[1.0, Times[Complex[-0.7500000000000001, -1.2990381056766578], genJacobiellk]], -1], genJacobiellk]]
 Test Values: {Rule[k, 1], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[r, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[-1.0, Times[Complex[-1.5000000000000002, -0.5980762113533156], Power[Plus[1.0, Times[Complex[-1.5000000000000002, -2.5980762113533156], genJacobiellk]], -1], genJacobiellk]]
 Test Values: {Rule[k, 2], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[r, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |}
 </div>

22.6: Difference between revisions

Latest revision as of 11:57, 28 June 2021

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