Jacobian Elliptic Functions - 22.17 Moduli Outside the Interval [0,1]

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
22.17.E1	${\displaystyle{\displaystyle\operatorname{pq}\left(z,k\right)=\operatorname{pq}\left(z,-k\right)}}$ \genJacobiellk{p}{q}@{z}{k} = \genJacobiellk{p}{q}@{z}{-k}		genJacobiellk(p)*q* z*k = genJacobiellk(p)*q* z- k	genJacobiellk[p]*q* z*k == genJacobiellk[p]*q* z- k	Failure	Failure	Error	Failed [300 / 300] Result: 1.0 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[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Plus[2.0, Times[Complex[0.0, 1.0], 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[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
22.17.E2	${\displaystyle{\displaystyle\operatorname{sn}\left(z,1/k\right)=k\operatorname{sn}\left(z/k,k\right)}}$ \Jacobiellsnk@{z}{1/k} = k\Jacobiellsnk@{z/k}{k}		JacobiSN(z, 1/k) = k*JacobiSN(z/k, k)	JacobiSN[z, (1/k)^2] == k*JacobiSN[z/k, (k)^2]	Failure	Failure	Successful [Tested: 21]	Successful [Tested: 21]
22.17.E3	${\displaystyle{\displaystyle\operatorname{cn}\left(z,1/k\right)=\operatorname{dn}\left(z/k,k\right)}}$ \Jacobiellcnk@{z}{1/k} = \Jacobielldnk@{z/k}{k}		JacobiCN(z, 1/k) = JacobiDN(z/k, k)	JacobiCN[z, (1/k)^2] == JacobiDN[z/k, (k)^2]	Failure	Failure	Successful [Tested: 21]	Successful [Tested: 21]
22.17.E4	${\displaystyle{\displaystyle\operatorname{dn}\left(z,1/k\right)=\operatorname{cn}\left(z/k,k\right)}}$ \Jacobielldnk@{z}{1/k} = \Jacobiellcnk@{z/k}{k}		JacobiDN(z, 1/k) = JacobiCN(z/k, k)	JacobiDN[z, (1/k)^2] == JacobiCN[z/k, (k)^2]	Failure	Failure	Successful [Tested: 21]	Successful [Tested: 21]