29.6: Difference between revisions

Latest revision as of 12:09, 28 June 2021

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
29.6.E5	${\displaystyle{\displaystyle\tfrac{1}{2}A_{0}^{2}+\sum_{p=1}^{\infty}A_{2p}^{2% }=1}}$ `\tfrac{1}{2}A_{0}^{2}+\sum_{p=1}^{\infty}A_{2p}^{2} = 1`		(1)/(2)(A[0])^(2)+ sum((A[2p])^(2), p = 1..infinity) = 1	Divide[1,2](Subscript[A, 0])^(2)+ Sum[(Subscript[A, 2p])^(2), {p, 1, Infinity}, GenerateConditions->None] == 1	Skipped - no semantic math	Skipped - no semantic math	-	-
29.6.E6	${\displaystyle{\displaystyle\tfrac{1}{2}A_{0}+\sum_{p=1}^{\infty}A_{2p}>0}}$ `\tfrac{1}{2}A_{0}+\sum_{p=1}^{\infty}A_{2p} > 0`		(1)/(2)A[0]+ sum(A[2p], p = 1..infinity) > 0	Divide[1,2]Subscript[A, 0]+ Sum[Subscript[A, 2p], {p, 1, Infinity}, GenerateConditions->None] > 0	Skipped - no semantic math	Skipped - no semantic math	-	-
29.6.E7	${\displaystyle{\displaystyle\lim_{p\to\infty}\frac{A_{2p+2}}{A_{2p}}=\frac{k^{% 2}}{(1+k^{\prime})^{2}}}}$ `\lim_{p\to\infty}\frac{A_{2p+2}}{A_{2p}} = \frac{k^{2}}{(1+k^{\prime})^{2}}`	${\displaystyle{\displaystyle\nu\neq 2n,\nu=2n,m>n}}$	limit((A[2p + 2])/(A[2p]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2))	Limit[Divide[Subscript[A, 2p + 2],Subscript[A, 2p]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)]	Skipped - no semantic math	Skipped - no semantic math	-	-
29.6#Ex2	${\displaystyle{\displaystyle\beta_{p}=4p^{2}(2-k^{2})}}$ `\beta_{p} = 4p^{2}(2-k^{2})`		beta[p] = 4(p)^(2)(2 - (k)^(2))	Subscript[\[Beta], p] == 4(p)^(2)(2 - (k)^(2))	Skipped - no semantic math	Skipped - no semantic math	-	-
29.6#Ex3	${\displaystyle{\displaystyle\gamma_{p}=\tfrac{1}{2}(\nu-2p+1)(\nu+2p)k^{2}}}$ `\gamma_{p} = \tfrac{1}{2}(\nu-2p+1)(\nu+2p)k^{2}`		((1)/(2)(nu - 2p + 2)(nu + 2p - 1)(k)^(2)) = (1)/(2)(nu - 2p + 1)(nu + 2p)(k)^(2)	(Divide[1,2](\[Nu]- 2p + 2)(\[Nu]+ 2p - 1)(k)^(2)) == Divide[1,2](\[Nu]- 2p + 1)(\[Nu]+ 2p)(k)^(2)	Skipped - no semantic math	Skipped - no semantic math	-	-
29.6.E12	${\displaystyle{\displaystyle\left(1-\tfrac{1}{2}k^{2}\right)\left(\tfrac{1}{2}% C_{0}^{2}+\sum_{p=1}^{\infty}C_{2p}^{2}\right)-\tfrac{1}{2}k^{2}\sum_{p=0}^{% \infty}C_{2p}C_{2p+2}=1}}$ `\left(1-\tfrac{1}{2}k^{2}\right)\left(\tfrac{1}{2}C_{0}^{2}+\sum_{p=1}^{\infty}C_{2p}^{2}\right)-\tfrac{1}{2}k^{2}\sum_{p=0}^{\infty}C_{2p}C_{2p+2} = 1`		(1 -(1)/(2)(k)^(2))((1)/(2)(C[0])^(2)+ sum((C[2p])^(2), p = 1..infinity))-(1)/(2)(k)^(2) sum(C[2p]C[2*p + 2], p = 0..infinity) = 1	(1 -Divide[1,2](k)^(2))(Divide[1,2](Subscript[C, 0])^(2)+ Sum[(Subscript[C, 2p])^(2), {p, 1, Infinity}, GenerateConditions->None])-Divide[1,2](k)^(2) Sum[Subscript[C, 2p]Subscript[C, 2*p + 2], {p, 0, Infinity}, GenerateConditions->None] == 1	Skipped - no semantic math	Skipped - no semantic math	-	-
29.6.E13	${\displaystyle{\displaystyle\tfrac{1}{2}C_{0}+\sum_{p=1}^{\infty}C_{2p}>0}}$ `\tfrac{1}{2}C_{0}+\sum_{p=1}^{\infty}C_{2p} > 0`		(1)/(2)C[0]+ sum(C[2p], p = 1..infinity) > 0	Divide[1,2]Subscript[C, 0]+ Sum[Subscript[C, 2p], {p, 1, Infinity}, GenerateConditions->None] > 0	Skipped - no semantic math	Skipped - no semantic math	-	-
29.6.E14	${\displaystyle{\displaystyle\lim_{p\to\infty}\frac{C_{2p+2}}{C_{2p}}=\frac{k^{% 2}}{(1+k^{\prime})^{2}}}}$ `\lim_{p\to\infty}\frac{C_{2p+2}}{C_{2p}} = \frac{k^{2}}{(1+k^{\prime})^{2}}`	${\displaystyle{\displaystyle\nu\neq 2n+1,\nu=2n+1,m>n}}$	limit((C[2p + 2])/(C[2p]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2))	Limit[Divide[Subscript[C, 2p + 2],Subscript[C, 2p]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)]	Skipped - no semantic math	Skipped - no semantic math	-	-
29.6.E20	${\displaystyle{\displaystyle\sum_{p=0}^{\infty}A_{2p+1}^{2}=1}}$ `\sum_{p=0}^{\infty}A_{2p+1}^{2} = 1`		sum((A[2*p + 1])^(2), p = 0..infinity) = 1	Sum[(Subscript[A, 2*p + 1])^(2), {p, 0, Infinity}, GenerateConditions->None] == 1	Skipped - no semantic math	Skipped - no semantic math	-	-
29.6.E21	${\displaystyle{\displaystyle\sum_{p=0}^{\infty}A_{2p+1}>0}}$ `\sum_{p=0}^{\infty}A_{2p+1} > 0`		sum(A[2*p + 1], p = 0..infinity) > 0	Sum[Subscript[A, 2*p + 1], {p, 0, Infinity}, GenerateConditions->None] > 0	Skipped - no semantic math	Skipped - no semantic math	-	-
29.6.E22	${\displaystyle{\displaystyle\lim_{p\to\infty}\frac{A_{2p+1}}{A_{2p-1}}=\frac{k% ^{2}}{(1+k^{\prime})^{2}}}}$ `\lim_{p\to\infty}\frac{A_{2p+1}}{A_{2p-1}} = \frac{k^{2}}{(1+k^{\prime})^{2}}`	${\displaystyle{\displaystyle\nu\neq 2n+1,\nu=2n+1,m>n}}$	limit((A[2p + 1])/(A[2p - 1]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2))	Limit[Divide[Subscript[A, 2p + 1],Subscript[A, 2p - 1]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)]	Skipped - no semantic math	Skipped - no semantic math	-	-
29.6#Ex4	${\displaystyle{\displaystyle\alpha_{p}=\tfrac{1}{2}(\nu-2p-1)(\nu+2p+2)k^{2}}}$ `\alpha_{p} = \tfrac{1}{2}(\nu-2p-1)(\nu+2p+2)k^{2}`		alpha[p] = (1)/(2)(nu - 2p - 1)(nu + 2p + 2)*(k)^(2)	Subscript[\[Alpha], p] == Divide[1,2](\[Nu]- 2p - 1)(\[Nu]+ 2p + 2)*(k)^(2)	Skipped - no semantic math	Skipped - no semantic math	-	-
29.6#Ex6	${\displaystyle{\displaystyle\gamma_{p}=\tfrac{1}{2}(\nu-2p)(\nu+2p+1)k^{2}}}$ `\gamma_{p} = \tfrac{1}{2}(\nu-2p)(\nu+2p+1)k^{2}`		((1)/(2)(nu - 2p + 2)(nu + 2p - 1)(k)^(2)) = (1)/(2)(nu - 2p)(nu + 2p + 1)(k)^(2)	(Divide[1,2](\[Nu]- 2p + 2)(\[Nu]+ 2p - 1)(k)^(2)) == Divide[1,2](\[Nu]- 2p)(\[Nu]+ 2p + 1)(k)^(2)	Skipped - no semantic math	Skipped - no semantic math	-	-
29.6.E28	${\displaystyle{\displaystyle\sum_{p=0}^{\infty}C_{2p+1}>0}}$ `\sum_{p=0}^{\infty}C_{2p+1} > 0`		sum(C[2*p + 1], p = 0..infinity) > 0	Sum[Subscript[C, 2*p + 1], {p, 0, Infinity}, GenerateConditions->None] > 0	Skipped - no semantic math	Skipped - no semantic math	-	-
29.6.E29	${\displaystyle{\displaystyle\lim_{p\to\infty}\frac{C_{2p+1}}{C_{2p-1}}=\frac{k% ^{2}}{(1+k^{\prime})^{2}}}}$ `\lim_{p\to\infty}\frac{C_{2p+1}}{C_{2p-1}} = \frac{k^{2}}{(1+k^{\prime})^{2}}`	${\displaystyle{\displaystyle\nu\neq 2n+2,\nu=2n+2,m>n}}$	limit((C[2p + 1])/(C[2p - 1]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2))	Limit[Divide[Subscript[C, 2p + 1],Subscript[C, 2p - 1]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)]	Skipped - no semantic math	Skipped - no semantic math	-	-
29.6.E35	${\displaystyle{\displaystyle\sum_{p=0}^{\infty}B_{2p+1}^{2}=1}}$ `\sum_{p=0}^{\infty}B_{2p+1}^{2} = 1`		sum((B[2*p + 1])^(2), p = 0..infinity) = 1	Sum[(Subscript[B, 2*p + 1])^(2), {p, 0, Infinity}, GenerateConditions->None] == 1	Skipped - no semantic math	Skipped - no semantic math	-	-
29.6.E36	${\displaystyle{\displaystyle\sum_{p=0}^{\infty}(2p+1)B_{2p+1}>0}}$ `\sum_{p=0}^{\infty}(2p+1)B_{2p+1} > 0`		sum((2p + 1)B[2*p + 1], p = 0..infinity) > 0	Sum[(2p + 1)Subscript[B, 2*p + 1], {p, 0, Infinity}, GenerateConditions->None] > 0	Skipped - no semantic math	Skipped - no semantic math	-	-
29.6.E37	${\displaystyle{\displaystyle\lim_{p\to\infty}\frac{B_{2p+1}}{B_{2p-1}}=\frac{k% ^{2}}{(1+k^{\prime})^{2}}}}$ `\lim_{p\to\infty}\frac{B_{2p+1}}{B_{2p-1}} = \frac{k^{2}}{(1+k^{\prime})^{2}}`	${\displaystyle{\displaystyle\nu\neq 2n+1,\nu=2n+1,m>n}}$	limit((B[2p + 1])/(B[2p - 1]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2))	Limit[Divide[Subscript[B, 2p + 1],Subscript[B, 2p - 1]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)]	Skipped - no semantic math	Skipped - no semantic math	-	-
29.6#Ex7	${\displaystyle{\displaystyle\alpha_{p}=\tfrac{1}{2}(\nu-2p-1)(\nu+2p+2)k^{2}}}$ `\alpha_{p} = \tfrac{1}{2}(\nu-2p-1)(\nu+2p+2)k^{2}`		alpha[p] = (1)/(2)(nu - 2p - 1)(nu + 2p + 2)*(k)^(2)	Subscript[\[Alpha], p] == Divide[1,2](\[Nu]- 2p - 1)(\[Nu]+ 2p + 2)*(k)^(2)	Skipped - no semantic math	Skipped - no semantic math	-	-
29.6#Ex9	${\displaystyle{\displaystyle\gamma_{p}=\tfrac{1}{2}(\nu-2p)(\nu+2p+1)k^{2}}}$ `\gamma_{p} = \tfrac{1}{2}(\nu-2p)(\nu+2p+1)k^{2}`		((1)/(2)(nu - 2p + 2)(nu + 2p - 1)(k)^(2)) = (1)/(2)(nu - 2p)(nu + 2p + 1)(k)^(2)	(Divide[1,2](\[Nu]- 2p + 2)(\[Nu]+ 2p - 1)(k)^(2)) == Divide[1,2](\[Nu]- 2p)(\[Nu]+ 2p + 1)(k)^(2)	Skipped - no semantic math	Skipped - no semantic math	-	-
29.6.E43	${\displaystyle{\displaystyle\sum_{p=0}^{\infty}(2p+1)D_{2p+1}>0}}$ `\sum_{p=0}^{\infty}(2p+1)D_{2p+1} > 0`		sum((2p + 1)D[2*p + 1], p = 0..infinity) > 0	Sum[(2p + 1)Subscript[D, 2*p + 1], {p, 0, Infinity}, GenerateConditions->None] > 0	Skipped - no semantic math	Skipped - no semantic math	-	-
29.6.E44	${\displaystyle{\displaystyle\lim_{p\to\infty}\frac{D_{2p+1}}{D_{2p-1}}=\frac{k% ^{2}}{(1+k^{\prime})^{2}}}}$ `\lim_{p\to\infty}\frac{D_{2p+1}}{D_{2p-1}} = \frac{k^{2}}{(1+k^{\prime})^{2}}`	${\displaystyle{\displaystyle\nu\neq 2n+2,\nu=2n+2,m>n}}$	limit((D[2p + 1])/(D[2p - 1]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2))	Limit[Divide[Subscript[D, 2p + 1],Subscript[D, 2p - 1]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)]	Skipped - no semantic math	Skipped - no semantic math	-	-
29.6.E50	${\displaystyle{\displaystyle\sum_{p=1}^{\infty}B_{2p}^{2}=1}}$ `\sum_{p=1}^{\infty}B_{2p}^{2} = 1`		sum((B[2*p])^(2), p = 1..infinity) = 1	Sum[(Subscript[B, 2*p])^(2), {p, 1, Infinity}, GenerateConditions->None] == 1	Skipped - no semantic math	Skipped - no semantic math	-	-
29.6.E51	${\displaystyle{\displaystyle\sum_{p=0}^{\infty}(2p+2)B_{2p+2}>0}}$ `\sum_{p=0}^{\infty}(2p+2)B_{2p+2} > 0`		sum((2p + 2)B[2*p + 2], p = 0..infinity) > 0	Sum[(2p + 2)Subscript[B, 2*p + 2], {p, 0, Infinity}, GenerateConditions->None] > 0	Skipped - no semantic math	Skipped - no semantic math	-	-
29.6.E52	${\displaystyle{\displaystyle\lim_{p\to\infty}\frac{B_{2p+2}}{B_{2p}}=\frac{k^{% 2}}{(1+k^{\prime})^{2}}}}$ `\lim_{p\to\infty}\frac{B_{2p+2}}{B_{2p}} = \frac{k^{2}}{(1+k^{\prime})^{2}}`	${\displaystyle{\displaystyle\nu\neq 2n+2,\nu=2n+2,m>n}}$	limit((B[2p + 2])/(B[2p]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2))	Limit[Divide[Subscript[B, 2p + 2],Subscript[B, 2p]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)]	Skipped - no semantic math	Skipped - no semantic math	-	-
29.6#Ex10	${\displaystyle{\displaystyle\alpha_{p}=\tfrac{1}{2}(\nu-2p-2)(\nu+2p+3)k^{2}}}$ `\alpha_{p} = \tfrac{1}{2}(\nu-2p-2)(\nu+2p+3)k^{2}`		alpha[p] = (1)/(2)(nu - 2p - 2)(nu + 2p + 3)*(k)^(2)	Subscript[\[Alpha], p] == Divide[1,2](\[Nu]- 2p - 2)(\[Nu]+ 2p + 3)*(k)^(2)	Skipped - no semantic math	Skipped - no semantic math	-	-
29.6#Ex11	${\displaystyle{\displaystyle\beta_{p}=(2p+2)^{2}(2-k^{2})}}$ `\beta_{p} = (2p+2)^{2}(2-k^{2})`		beta[p] = (2p + 2)^(2)(2 - (k)^(2))	Subscript[\[Beta], p] == (2p + 2)^(2)(2 - (k)^(2))	Skipped - no semantic math	Skipped - no semantic math	-	-
29.6#Ex12	${\displaystyle{\displaystyle\gamma_{p}=\tfrac{1}{2}(\nu-2p-1)(\nu+2p+2)k^{2}}}$ `\gamma_{p} = \tfrac{1}{2}(\nu-2p-1)(\nu+2p+2)k^{2}`		((1)/(2)(nu - 2p + 2)(nu + 2p - 1)(k)^(2)) = (1)/(2)(nu - 2p - 1)(nu + 2p + 2)(k)^(2)	(Divide[1,2](\[Nu]- 2p + 2)(\[Nu]+ 2p - 1)(k)^(2)) == Divide[1,2](\[Nu]- 2p - 1)(\[Nu]+ 2p + 2)(k)^(2)	Skipped - no semantic math	Skipped - no semantic math	-	-
29.6.E57	${\displaystyle{\displaystyle\left(1-\tfrac{1}{2}k^{2}\right)\sum_{p=1}^{\infty% }D_{2p}^{2}-\tfrac{1}{2}k^{2}\sum_{p=1}^{\infty}D_{2p}D_{2p+2}=1}}$ `\left(1-\tfrac{1}{2}k^{2}\right)\sum_{p=1}^{\infty}D_{2p}^{2}-\tfrac{1}{2}k^{2}\sum_{p=1}^{\infty}D_{2p}D_{2p+2} = 1`		(1 -(1)/(2)(k)^(2))sum((D[2p])^(2), p = 1..infinity)-(1)/(2)(k)^(2)* sum(D[2p]D[2*p + 2], p = 1..infinity) = 1	(1 -Divide[1,2](k)^(2))Sum[(Subscript[D, 2p])^(2), {p, 1, Infinity}, GenerateConditions->None]-Divide[1,2](k)^(2)* Sum[Subscript[D, 2p]Subscript[D, 2*p + 2], {p, 1, Infinity}, GenerateConditions->None] == 1	Skipped - no semantic math	Skipped - no semantic math	-	-
29.6.E58	${\displaystyle{\displaystyle\sum_{p=0}^{\infty}(2p+2)D_{2p+2}>0}}$ `\sum_{p=0}^{\infty}(2p+2)D_{2p+2} > 0`		sum((2p + 2)D[2*p + 2], p = 0..infinity) > 0	Sum[(2p + 2)Subscript[D, 2*p + 2], {p, 0, Infinity}, GenerateConditions->None] > 0	Skipped - no semantic math	Skipped - no semantic math	-	-
29.6.E59	${\displaystyle{\displaystyle\lim_{p\to\infty}\frac{D_{2p+2}}{D_{2p}}=\frac{k^{% 2}}{(1+k^{\prime})^{2}}}}$ `\lim_{p\to\infty}\frac{D_{2p+2}}{D_{2p}} = \frac{k^{2}}{(1+k^{\prime})^{2}}`	${\displaystyle{\displaystyle\nu\neq 2n+3,\nu=2n+3,m>n}}$	limit((D[2p + 2])/(D[2p]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2))	Limit[Divide[Subscript[D, 2p + 2],Subscript[D, 2p]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)]	Skipped - no semantic math	Skipped - no semantic math	-	-

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 ! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
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-| [https://dlmf.nist.gov/29.6.E5 29.6.E5] || [[Item:Q8631|<math>\tfrac{1}{2}A_{0}^{2}+\sum_{p=1}^{\infty}A_{2p}^{2} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\tfrac{1}{2}A_{0}^{2}+\sum_{p=1}^{\infty}A_{2p}^{2} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(1)/(2)*(A[0])^(2)+ sum((A[2*p])^(2), p = 1..infinity) = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Divide[1,2]*(Subscript[A, 0])^(2)+ Sum[(Subscript[A, 2*p])^(2), {p, 1, Infinity}, GenerateConditions->None] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/29.6.E5 29.6.E5] || <math qid="Q8631">\tfrac{1}{2}A_{0}^{2}+\sum_{p=1}^{\infty}A_{2p}^{2} = 1</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\tfrac{1}{2}A_{0}^{2}+\sum_{p=1}^{\infty}A_{2p}^{2} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(1)/(2)*(A[0])^(2)+ sum((A[2*p])^(2), p = 1..infinity) = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Divide[1,2]*(Subscript[A, 0])^(2)+ Sum[(Subscript[A, 2*p])^(2), {p, 1, Infinity}, GenerateConditions->None] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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-| [https://dlmf.nist.gov/29.6.E6 29.6.E6] || [[Item:Q8632|<math>\tfrac{1}{2}A_{0}+\sum_{p=1}^{\infty}A_{2p} > 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\tfrac{1}{2}A_{0}+\sum_{p=1}^{\infty}A_{2p} > 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(1)/(2)*A[0]+ sum(A[2*p], p = 1..infinity) > 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Divide[1,2]*Subscript[A, 0]+ Sum[Subscript[A, 2*p], {p, 1, Infinity}, GenerateConditions->None] > 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/29.6.E6 29.6.E6] || <math qid="Q8632">\tfrac{1}{2}A_{0}+\sum_{p=1}^{\infty}A_{2p} > 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\tfrac{1}{2}A_{0}+\sum_{p=1}^{\infty}A_{2p} > 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(1)/(2)*A[0]+ sum(A[2*p], p = 1..infinity) > 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Divide[1,2]*Subscript[A, 0]+ Sum[Subscript[A, 2*p], {p, 1, Infinity}, GenerateConditions->None] > 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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-| [https://dlmf.nist.gov/29.6.E7 29.6.E7] || [[Item:Q8633|<math>\lim_{p\to\infty}\frac{A_{2p+2}}{A_{2p}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lim_{p\to\infty}\frac{A_{2p+2}}{A_{2p}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</syntaxhighlight> || <math>\nu \neq 2n, \nu = 2n, m > n</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">limit((A[2*p + 2])/(A[2*p]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Limit[Divide[Subscript[A, 2*p + 2],Subscript[A, 2*p]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/29.6.E7 29.6.E7] || <math qid="Q8633">\lim_{p\to\infty}\frac{A_{2p+2}}{A_{2p}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lim_{p\to\infty}\frac{A_{2p+2}}{A_{2p}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</syntaxhighlight> || <math>\nu \neq 2n, \nu = 2n, m > n</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">limit((A[2*p + 2])/(A[2*p]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Limit[Divide[Subscript[A, 2*p + 2],Subscript[A, 2*p]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6#Ex2 29.6#Ex2] || [[Item:Q8638|<math>\beta_{p} = 4p^{2}(2-k^{2})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\beta_{p} = 4p^{2}(2-k^{2})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">beta[p] = 4*(p)^(2)*(2 - (k)^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Beta], p] == 4*(p)^(2)*(2 - (k)^(2))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/29.6#Ex2 29.6#Ex2] || <math qid="Q8638">\beta_{p} = 4p^{2}(2-k^{2})</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\beta_{p} = 4p^{2}(2-k^{2})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">beta[p] = 4*(p)^(2)*(2 - (k)^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Beta], p] == 4*(p)^(2)*(2 - (k)^(2))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6#Ex3 29.6#Ex3] || [[Item:Q8639|<math>\gamma_{p} = \tfrac{1}{2}(\nu-2p+1)(\nu+2p)k^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\gamma_{p} = \tfrac{1}{2}(\nu-2p+1)(\nu+2p)k^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">((1)/(2)*(nu - 2*p + 2)*(nu + 2*p - 1)*(k)^(2)) = (1)/(2)*(nu - 2*p + 1)*(nu + 2*p)*(k)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Divide[1,2]*(\[Nu]- 2*p + 2)*(\[Nu]+ 2*p - 1)*(k)^(2)) == Divide[1,2]*(\[Nu]- 2*p + 1)*(\[Nu]+ 2*p)*(k)^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/29.6#Ex3 29.6#Ex3] || <math qid="Q8639">\gamma_{p} = \tfrac{1}{2}(\nu-2p+1)(\nu+2p)k^{2}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\gamma_{p} = \tfrac{1}{2}(\nu-2p+1)(\nu+2p)k^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">((1)/(2)*(nu - 2*p + 2)*(nu + 2*p - 1)*(k)^(2)) = (1)/(2)*(nu - 2*p + 1)*(nu + 2*p)*(k)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Divide[1,2]*(\[Nu]- 2*p + 2)*(\[Nu]+ 2*p - 1)*(k)^(2)) == Divide[1,2]*(\[Nu]- 2*p + 1)*(\[Nu]+ 2*p)*(k)^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6.E12 29.6.E12] || [[Item:Q8640|<math>\left(1-\tfrac{1}{2}k^{2}\right)\left(\tfrac{1}{2}C_{0}^{2}+\sum_{p=1}^{\infty}C_{2p}^{2}\right)-\tfrac{1}{2}k^{2}\sum_{p=0}^{\infty}C_{2p}C_{2p+2} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\left(1-\tfrac{1}{2}k^{2}\right)\left(\tfrac{1}{2}C_{0}^{2}+\sum_{p=1}^{\infty}C_{2p}^{2}\right)-\tfrac{1}{2}k^{2}\sum_{p=0}^{\infty}C_{2p}C_{2p+2} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(1 -(1)/(2)*(k)^(2))*((1)/(2)*(C[0])^(2)+ sum((C[2*p])^(2), p = 1..infinity))-(1)/(2)*(k)^(2)* sum(C[2*p]*C[2*p + 2], p = 0..infinity) = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(1 -Divide[1,2]*(k)^(2))*(Divide[1,2]*(Subscript[C, 0])^(2)+ Sum[(Subscript[C, 2*p])^(2), {p, 1, Infinity}, GenerateConditions->None])-Divide[1,2]*(k)^(2)* Sum[Subscript[C, 2*p]*Subscript[C, 2*p + 2], {p, 0, Infinity}, GenerateConditions->None] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/29.6.E12 29.6.E12] || <math qid="Q8640">\left(1-\tfrac{1}{2}k^{2}\right)\left(\tfrac{1}{2}C_{0}^{2}+\sum_{p=1}^{\infty}C_{2p}^{2}\right)-\tfrac{1}{2}k^{2}\sum_{p=0}^{\infty}C_{2p}C_{2p+2} = 1</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\left(1-\tfrac{1}{2}k^{2}\right)\left(\tfrac{1}{2}C_{0}^{2}+\sum_{p=1}^{\infty}C_{2p}^{2}\right)-\tfrac{1}{2}k^{2}\sum_{p=0}^{\infty}C_{2p}C_{2p+2} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(1 -(1)/(2)*(k)^(2))*((1)/(2)*(C[0])^(2)+ sum((C[2*p])^(2), p = 1..infinity))-(1)/(2)*(k)^(2)* sum(C[2*p]*C[2*p + 2], p = 0..infinity) = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(1 -Divide[1,2]*(k)^(2))*(Divide[1,2]*(Subscript[C, 0])^(2)+ Sum[(Subscript[C, 2*p])^(2), {p, 1, Infinity}, GenerateConditions->None])-Divide[1,2]*(k)^(2)* Sum[Subscript[C, 2*p]*Subscript[C, 2*p + 2], {p, 0, Infinity}, GenerateConditions->None] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6.E13 29.6.E13] || [[Item:Q8641|<math>\tfrac{1}{2}C_{0}+\sum_{p=1}^{\infty}C_{2p} > 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\tfrac{1}{2}C_{0}+\sum_{p=1}^{\infty}C_{2p} > 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(1)/(2)*C[0]+ sum(C[2*p], p = 1..infinity) > 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Divide[1,2]*Subscript[C, 0]+ Sum[Subscript[C, 2*p], {p, 1, Infinity}, GenerateConditions->None] > 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/29.6.E13 29.6.E13] || <math qid="Q8641">\tfrac{1}{2}C_{0}+\sum_{p=1}^{\infty}C_{2p} > 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\tfrac{1}{2}C_{0}+\sum_{p=1}^{\infty}C_{2p} > 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(1)/(2)*C[0]+ sum(C[2*p], p = 1..infinity) > 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Divide[1,2]*Subscript[C, 0]+ Sum[Subscript[C, 2*p], {p, 1, Infinity}, GenerateConditions->None] > 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6.E14 29.6.E14] || [[Item:Q8642|<math>\lim_{p\to\infty}\frac{C_{2p+2}}{C_{2p}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lim_{p\to\infty}\frac{C_{2p+2}}{C_{2p}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</syntaxhighlight> || <math>\nu \neq 2n+1, \nu = 2n+1, m > n</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">limit((C[2*p + 2])/(C[2*p]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Limit[Divide[Subscript[C, 2*p + 2],Subscript[C, 2*p]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/29.6.E14 29.6.E14] || <math qid="Q8642">\lim_{p\to\infty}\frac{C_{2p+2}}{C_{2p}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lim_{p\to\infty}\frac{C_{2p+2}}{C_{2p}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</syntaxhighlight> || <math>\nu \neq 2n+1, \nu = 2n+1, m > n</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">limit((C[2*p + 2])/(C[2*p]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Limit[Divide[Subscript[C, 2*p + 2],Subscript[C, 2*p]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6.E20 29.6.E20] || [[Item:Q8648|<math>\sum_{p=0}^{\infty}A_{2p+1}^{2} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{p=0}^{\infty}A_{2p+1}^{2} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum((A[2*p + 1])^(2), p = 0..infinity) = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[(Subscript[A, 2*p + 1])^(2), {p, 0, Infinity}, GenerateConditions->None] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/29.6.E20 29.6.E20] || <math qid="Q8648">\sum_{p=0}^{\infty}A_{2p+1}^{2} = 1</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{p=0}^{\infty}A_{2p+1}^{2} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum((A[2*p + 1])^(2), p = 0..infinity) = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[(Subscript[A, 2*p + 1])^(2), {p, 0, Infinity}, GenerateConditions->None] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6.E21 29.6.E21] || [[Item:Q8649|<math>\sum_{p=0}^{\infty}A_{2p+1} > 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{p=0}^{\infty}A_{2p+1} > 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum(A[2*p + 1], p = 0..infinity) > 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[Subscript[A, 2*p + 1], {p, 0, Infinity}, GenerateConditions->None] > 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/29.6.E21 29.6.E21] || <math qid="Q8649">\sum_{p=0}^{\infty}A_{2p+1} > 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{p=0}^{\infty}A_{2p+1} > 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum(A[2*p + 1], p = 0..infinity) > 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[Subscript[A, 2*p + 1], {p, 0, Infinity}, GenerateConditions->None] > 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6.E22 29.6.E22] || [[Item:Q8650|<math>\lim_{p\to\infty}\frac{A_{2p+1}}{A_{2p-1}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lim_{p\to\infty}\frac{A_{2p+1}}{A_{2p-1}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</syntaxhighlight> || <math>\nu \neq 2n+1, \nu = 2n+1, m > n</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">limit((A[2*p + 1])/(A[2*p - 1]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Limit[Divide[Subscript[A, 2*p + 1],Subscript[A, 2*p - 1]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/29.6.E22 29.6.E22] || <math qid="Q8650">\lim_{p\to\infty}\frac{A_{2p+1}}{A_{2p-1}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lim_{p\to\infty}\frac{A_{2p+1}}{A_{2p-1}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</syntaxhighlight> || <math>\nu \neq 2n+1, \nu = 2n+1, m > n</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">limit((A[2*p + 1])/(A[2*p - 1]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Limit[Divide[Subscript[A, 2*p + 1],Subscript[A, 2*p - 1]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6#Ex4 29.6#Ex4] || [[Item:Q8654|<math>\alpha_{p} = \tfrac{1}{2}(\nu-2p-1)(\nu+2p+2)k^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha_{p} = \tfrac{1}{2}(\nu-2p-1)(\nu+2p+2)k^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha[p] = (1)/(2)*(nu - 2*p - 1)*(nu + 2*p + 2)*(k)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Alpha], p] == Divide[1,2]*(\[Nu]- 2*p - 1)*(\[Nu]+ 2*p + 2)*(k)^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/29.6#Ex4 29.6#Ex4] || <math qid="Q8654">\alpha_{p} = \tfrac{1}{2}(\nu-2p-1)(\nu+2p+2)k^{2}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha_{p} = \tfrac{1}{2}(\nu-2p-1)(\nu+2p+2)k^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha[p] = (1)/(2)*(nu - 2*p - 1)*(nu + 2*p + 2)*(k)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Alpha], p] == Divide[1,2]*(\[Nu]- 2*p - 1)*(\[Nu]+ 2*p + 2)*(k)^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6#Ex6 29.6#Ex6] || [[Item:Q8656|<math>\gamma_{p} = \tfrac{1}{2}(\nu-2p)(\nu+2p+1)k^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\gamma_{p} = \tfrac{1}{2}(\nu-2p)(\nu+2p+1)k^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">((1)/(2)*(nu - 2*p + 2)*(nu + 2*p - 1)*(k)^(2)) = (1)/(2)*(nu - 2*p)*(nu + 2*p + 1)*(k)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Divide[1,2]*(\[Nu]- 2*p + 2)*(\[Nu]+ 2*p - 1)*(k)^(2)) == Divide[1,2]*(\[Nu]- 2*p)*(\[Nu]+ 2*p + 1)*(k)^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/29.6#Ex6 29.6#Ex6] || <math qid="Q8656">\gamma_{p} = \tfrac{1}{2}(\nu-2p)(\nu+2p+1)k^{2}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\gamma_{p} = \tfrac{1}{2}(\nu-2p)(\nu+2p+1)k^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">((1)/(2)*(nu - 2*p + 2)*(nu + 2*p - 1)*(k)^(2)) = (1)/(2)*(nu - 2*p)*(nu + 2*p + 1)*(k)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Divide[1,2]*(\[Nu]- 2*p + 2)*(\[Nu]+ 2*p - 1)*(k)^(2)) == Divide[1,2]*(\[Nu]- 2*p)*(\[Nu]+ 2*p + 1)*(k)^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6.E28 29.6.E28] || [[Item:Q8658|<math>\sum_{p=0}^{\infty}C_{2p+1} > 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{p=0}^{\infty}C_{2p+1} > 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum(C[2*p + 1], p = 0..infinity) > 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[Subscript[C, 2*p + 1], {p, 0, Infinity}, GenerateConditions->None] > 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/29.6.E28 29.6.E28] || <math qid="Q8658">\sum_{p=0}^{\infty}C_{2p+1} > 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{p=0}^{\infty}C_{2p+1} > 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum(C[2*p + 1], p = 0..infinity) > 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[Subscript[C, 2*p + 1], {p, 0, Infinity}, GenerateConditions->None] > 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6.E29 29.6.E29] || [[Item:Q8659|<math>\lim_{p\to\infty}\frac{C_{2p+1}}{C_{2p-1}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lim_{p\to\infty}\frac{C_{2p+1}}{C_{2p-1}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</syntaxhighlight> || <math>\nu \neq 2n+2, \nu = 2n+2, m > n</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">limit((C[2*p + 1])/(C[2*p - 1]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Limit[Divide[Subscript[C, 2*p + 1],Subscript[C, 2*p - 1]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/29.6.E29 29.6.E29] || <math qid="Q8659">\lim_{p\to\infty}\frac{C_{2p+1}}{C_{2p-1}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lim_{p\to\infty}\frac{C_{2p+1}}{C_{2p-1}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</syntaxhighlight> || <math>\nu \neq 2n+2, \nu = 2n+2, m > n</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">limit((C[2*p + 1])/(C[2*p - 1]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Limit[Divide[Subscript[C, 2*p + 1],Subscript[C, 2*p - 1]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6.E35 29.6.E35] || [[Item:Q8665|<math>\sum_{p=0}^{\infty}B_{2p+1}^{2} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{p=0}^{\infty}B_{2p+1}^{2} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum((B[2*p + 1])^(2), p = 0..infinity) = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[(Subscript[B, 2*p + 1])^(2), {p, 0, Infinity}, GenerateConditions->None] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/29.6.E35 29.6.E35] || <math qid="Q8665">\sum_{p=0}^{\infty}B_{2p+1}^{2} = 1</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{p=0}^{\infty}B_{2p+1}^{2} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum((B[2*p + 1])^(2), p = 0..infinity) = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[(Subscript[B, 2*p + 1])^(2), {p, 0, Infinity}, GenerateConditions->None] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6.E36 29.6.E36] || [[Item:Q8666|<math>\sum_{p=0}^{\infty}(2p+1)B_{2p+1} > 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{p=0}^{\infty}(2p+1)B_{2p+1} > 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum((2*p + 1)*B[2*p + 1], p = 0..infinity) > 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[(2*p + 1)*Subscript[B, 2*p + 1], {p, 0, Infinity}, GenerateConditions->None] > 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/29.6.E36 29.6.E36] || <math qid="Q8666">\sum_{p=0}^{\infty}(2p+1)B_{2p+1} > 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{p=0}^{\infty}(2p+1)B_{2p+1} > 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum((2*p + 1)*B[2*p + 1], p = 0..infinity) > 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[(2*p + 1)*Subscript[B, 2*p + 1], {p, 0, Infinity}, GenerateConditions->None] > 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6.E37 29.6.E37] || [[Item:Q8667|<math>\lim_{p\to\infty}\frac{B_{2p+1}}{B_{2p-1}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lim_{p\to\infty}\frac{B_{2p+1}}{B_{2p-1}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</syntaxhighlight> || <math>\nu \neq 2n+1, \nu = 2n+1, m > n</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">limit((B[2*p + 1])/(B[2*p - 1]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Limit[Divide[Subscript[B, 2*p + 1],Subscript[B, 2*p - 1]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/29.6.E37 29.6.E37] || <math qid="Q8667">\lim_{p\to\infty}\frac{B_{2p+1}}{B_{2p-1}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lim_{p\to\infty}\frac{B_{2p+1}}{B_{2p-1}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</syntaxhighlight> || <math>\nu \neq 2n+1, \nu = 2n+1, m > n</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">limit((B[2*p + 1])/(B[2*p - 1]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Limit[Divide[Subscript[B, 2*p + 1],Subscript[B, 2*p - 1]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6#Ex7 29.6#Ex7] || [[Item:Q8671|<math>\alpha_{p} = \tfrac{1}{2}(\nu-2p-1)(\nu+2p+2)k^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha_{p} = \tfrac{1}{2}(\nu-2p-1)(\nu+2p+2)k^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha[p] = (1)/(2)*(nu - 2*p - 1)*(nu + 2*p + 2)*(k)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Alpha], p] == Divide[1,2]*(\[Nu]- 2*p - 1)*(\[Nu]+ 2*p + 2)*(k)^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/29.6#Ex7 29.6#Ex7] || <math qid="Q8671">\alpha_{p} = \tfrac{1}{2}(\nu-2p-1)(\nu+2p+2)k^{2}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha_{p} = \tfrac{1}{2}(\nu-2p-1)(\nu+2p+2)k^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha[p] = (1)/(2)*(nu - 2*p - 1)*(nu + 2*p + 2)*(k)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Alpha], p] == Divide[1,2]*(\[Nu]- 2*p - 1)*(\[Nu]+ 2*p + 2)*(k)^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6#Ex9 29.6#Ex9] || [[Item:Q8673|<math>\gamma_{p} = \tfrac{1}{2}(\nu-2p)(\nu+2p+1)k^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\gamma_{p} = \tfrac{1}{2}(\nu-2p)(\nu+2p+1)k^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">((1)/(2)*(nu - 2*p + 2)*(nu + 2*p - 1)*(k)^(2)) = (1)/(2)*(nu - 2*p)*(nu + 2*p + 1)*(k)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Divide[1,2]*(\[Nu]- 2*p + 2)*(\[Nu]+ 2*p - 1)*(k)^(2)) == Divide[1,2]*(\[Nu]- 2*p)*(\[Nu]+ 2*p + 1)*(k)^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/29.6#Ex9 29.6#Ex9] || <math qid="Q8673">\gamma_{p} = \tfrac{1}{2}(\nu-2p)(\nu+2p+1)k^{2}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\gamma_{p} = \tfrac{1}{2}(\nu-2p)(\nu+2p+1)k^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">((1)/(2)*(nu - 2*p + 2)*(nu + 2*p - 1)*(k)^(2)) = (1)/(2)*(nu - 2*p)*(nu + 2*p + 1)*(k)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Divide[1,2]*(\[Nu]- 2*p + 2)*(\[Nu]+ 2*p - 1)*(k)^(2)) == Divide[1,2]*(\[Nu]- 2*p)*(\[Nu]+ 2*p + 1)*(k)^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6.E43 29.6.E43] || [[Item:Q8675|<math>\sum_{p=0}^{\infty}(2p+1)D_{2p+1} > 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{p=0}^{\infty}(2p+1)D_{2p+1} > 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum((2*p + 1)*D[2*p + 1], p = 0..infinity) > 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[(2*p + 1)*Subscript[D, 2*p + 1], {p, 0, Infinity}, GenerateConditions->None] > 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/29.6.E43 29.6.E43] || <math qid="Q8675">\sum_{p=0}^{\infty}(2p+1)D_{2p+1} > 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{p=0}^{\infty}(2p+1)D_{2p+1} > 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum((2*p + 1)*D[2*p + 1], p = 0..infinity) > 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[(2*p + 1)*Subscript[D, 2*p + 1], {p, 0, Infinity}, GenerateConditions->None] > 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6.E44 29.6.E44] || [[Item:Q8676|<math>\lim_{p\to\infty}\frac{D_{2p+1}}{D_{2p-1}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lim_{p\to\infty}\frac{D_{2p+1}}{D_{2p-1}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</syntaxhighlight> || <math>\nu \neq 2n+2, \nu = 2n+2, m > n</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">limit((D[2*p + 1])/(D[2*p - 1]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Limit[Divide[Subscript[D, 2*p + 1],Subscript[D, 2*p - 1]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/29.6.E44 29.6.E44] || <math qid="Q8676">\lim_{p\to\infty}\frac{D_{2p+1}}{D_{2p-1}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lim_{p\to\infty}\frac{D_{2p+1}}{D_{2p-1}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</syntaxhighlight> || <math>\nu \neq 2n+2, \nu = 2n+2, m > n</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">limit((D[2*p + 1])/(D[2*p - 1]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Limit[Divide[Subscript[D, 2*p + 1],Subscript[D, 2*p - 1]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6.E50 29.6.E50] || [[Item:Q8682|<math>\sum_{p=1}^{\infty}B_{2p}^{2} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{p=1}^{\infty}B_{2p}^{2} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum((B[2*p])^(2), p = 1..infinity) = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[(Subscript[B, 2*p])^(2), {p, 1, Infinity}, GenerateConditions->None] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/29.6.E50 29.6.E50] || <math qid="Q8682">\sum_{p=1}^{\infty}B_{2p}^{2} = 1</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{p=1}^{\infty}B_{2p}^{2} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum((B[2*p])^(2), p = 1..infinity) = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[(Subscript[B, 2*p])^(2), {p, 1, Infinity}, GenerateConditions->None] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6.E51 29.6.E51] || [[Item:Q8683|<math>\sum_{p=0}^{\infty}(2p+2)B_{2p+2} > 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{p=0}^{\infty}(2p+2)B_{2p+2} > 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum((2*p + 2)*B[2*p + 2], p = 0..infinity) > 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[(2*p + 2)*Subscript[B, 2*p + 2], {p, 0, Infinity}, GenerateConditions->None] > 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/29.6.E51 29.6.E51] || <math qid="Q8683">\sum_{p=0}^{\infty}(2p+2)B_{2p+2} > 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{p=0}^{\infty}(2p+2)B_{2p+2} > 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum((2*p + 2)*B[2*p + 2], p = 0..infinity) > 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[(2*p + 2)*Subscript[B, 2*p + 2], {p, 0, Infinity}, GenerateConditions->None] > 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6.E52 29.6.E52] || [[Item:Q8684|<math>\lim_{p\to\infty}\frac{B_{2p+2}}{B_{2p}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lim_{p\to\infty}\frac{B_{2p+2}}{B_{2p}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</syntaxhighlight> || <math>\nu \neq 2n+2, \nu = 2n+2, m > n</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">limit((B[2*p + 2])/(B[2*p]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Limit[Divide[Subscript[B, 2*p + 2],Subscript[B, 2*p]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/29.6.E52 29.6.E52] || <math qid="Q8684">\lim_{p\to\infty}\frac{B_{2p+2}}{B_{2p}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lim_{p\to\infty}\frac{B_{2p+2}}{B_{2p}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</syntaxhighlight> || <math>\nu \neq 2n+2, \nu = 2n+2, m > n</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">limit((B[2*p + 2])/(B[2*p]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Limit[Divide[Subscript[B, 2*p + 2],Subscript[B, 2*p]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6#Ex10 29.6#Ex10] || [[Item:Q8688|<math>\alpha_{p} = \tfrac{1}{2}(\nu-2p-2)(\nu+2p+3)k^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha_{p} = \tfrac{1}{2}(\nu-2p-2)(\nu+2p+3)k^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha[p] = (1)/(2)*(nu - 2*p - 2)*(nu + 2*p + 3)*(k)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Alpha], p] == Divide[1,2]*(\[Nu]- 2*p - 2)*(\[Nu]+ 2*p + 3)*(k)^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/29.6#Ex10 29.6#Ex10] || <math qid="Q8688">\alpha_{p} = \tfrac{1}{2}(\nu-2p-2)(\nu+2p+3)k^{2}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha_{p} = \tfrac{1}{2}(\nu-2p-2)(\nu+2p+3)k^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha[p] = (1)/(2)*(nu - 2*p - 2)*(nu + 2*p + 3)*(k)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Alpha], p] == Divide[1,2]*(\[Nu]- 2*p - 2)*(\[Nu]+ 2*p + 3)*(k)^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6#Ex11 29.6#Ex11] || [[Item:Q8689|<math>\beta_{p} = (2p+2)^{2}(2-k^{2})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\beta_{p} = (2p+2)^{2}(2-k^{2})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">beta[p] = (2*p + 2)^(2)*(2 - (k)^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Beta], p] == (2*p + 2)^(2)*(2 - (k)^(2))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/29.6#Ex11 29.6#Ex11] || <math qid="Q8689">\beta_{p} = (2p+2)^{2}(2-k^{2})</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\beta_{p} = (2p+2)^{2}(2-k^{2})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">beta[p] = (2*p + 2)^(2)*(2 - (k)^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Beta], p] == (2*p + 2)^(2)*(2 - (k)^(2))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6#Ex12 29.6#Ex12] || [[Item:Q8690|<math>\gamma_{p} = \tfrac{1}{2}(\nu-2p-1)(\nu+2p+2)k^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\gamma_{p} = \tfrac{1}{2}(\nu-2p-1)(\nu+2p+2)k^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">((1)/(2)*(nu - 2*p + 2)*(nu + 2*p - 1)*(k)^(2)) = (1)/(2)*(nu - 2*p - 1)*(nu + 2*p + 2)*(k)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Divide[1,2]*(\[Nu]- 2*p + 2)*(\[Nu]+ 2*p - 1)*(k)^(2)) == Divide[1,2]*(\[Nu]- 2*p - 1)*(\[Nu]+ 2*p + 2)*(k)^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/29.6#Ex12 29.6#Ex12] || <math qid="Q8690">\gamma_{p} = \tfrac{1}{2}(\nu-2p-1)(\nu+2p+2)k^{2}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\gamma_{p} = \tfrac{1}{2}(\nu-2p-1)(\nu+2p+2)k^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">((1)/(2)*(nu - 2*p + 2)*(nu + 2*p - 1)*(k)^(2)) = (1)/(2)*(nu - 2*p - 1)*(nu + 2*p + 2)*(k)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Divide[1,2]*(\[Nu]- 2*p + 2)*(\[Nu]+ 2*p - 1)*(k)^(2)) == Divide[1,2]*(\[Nu]- 2*p - 1)*(\[Nu]+ 2*p + 2)*(k)^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6.E57 29.6.E57] || [[Item:Q8691|<math>\left(1-\tfrac{1}{2}k^{2}\right)\sum_{p=1}^{\infty}D_{2p}^{2}-\tfrac{1}{2}k^{2}\sum_{p=1}^{\infty}D_{2p}D_{2p+2} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\left(1-\tfrac{1}{2}k^{2}\right)\sum_{p=1}^{\infty}D_{2p}^{2}-\tfrac{1}{2}k^{2}\sum_{p=1}^{\infty}D_{2p}D_{2p+2} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(1 -(1)/(2)*(k)^(2))*sum((D[2*p])^(2), p = 1..infinity)-(1)/(2)*(k)^(2)* sum(D[2*p]*D[2*p + 2], p = 1..infinity) = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(1 -Divide[1,2]*(k)^(2))*Sum[(Subscript[D, 2*p])^(2), {p, 1, Infinity}, GenerateConditions->None]-Divide[1,2]*(k)^(2)* Sum[Subscript[D, 2*p]*Subscript[D, 2*p + 2], {p, 1, Infinity}, GenerateConditions->None] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/29.6.E57 29.6.E57] || <math qid="Q8691">\left(1-\tfrac{1}{2}k^{2}\right)\sum_{p=1}^{\infty}D_{2p}^{2}-\tfrac{1}{2}k^{2}\sum_{p=1}^{\infty}D_{2p}D_{2p+2} = 1</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\left(1-\tfrac{1}{2}k^{2}\right)\sum_{p=1}^{\infty}D_{2p}^{2}-\tfrac{1}{2}k^{2}\sum_{p=1}^{\infty}D_{2p}D_{2p+2} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(1 -(1)/(2)*(k)^(2))*sum((D[2*p])^(2), p = 1..infinity)-(1)/(2)*(k)^(2)* sum(D[2*p]*D[2*p + 2], p = 1..infinity) = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(1 -Divide[1,2]*(k)^(2))*Sum[(Subscript[D, 2*p])^(2), {p, 1, Infinity}, GenerateConditions->None]-Divide[1,2]*(k)^(2)* Sum[Subscript[D, 2*p]*Subscript[D, 2*p + 2], {p, 1, Infinity}, GenerateConditions->None] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6.E58 29.6.E58] || [[Item:Q8692|<math>\sum_{p=0}^{\infty}(2p+2)D_{2p+2} > 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{p=0}^{\infty}(2p+2)D_{2p+2} > 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum((2*p + 2)*D[2*p + 2], p = 0..infinity) > 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[(2*p + 2)*Subscript[D, 2*p + 2], {p, 0, Infinity}, GenerateConditions->None] > 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/29.6.E58 29.6.E58] || <math qid="Q8692">\sum_{p=0}^{\infty}(2p+2)D_{2p+2} > 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{p=0}^{\infty}(2p+2)D_{2p+2} > 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum((2*p + 2)*D[2*p + 2], p = 0..infinity) > 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[(2*p + 2)*Subscript[D, 2*p + 2], {p, 0, Infinity}, GenerateConditions->None] > 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/29.6.E59 29.6.E59] || [[Item:Q8693|<math>\lim_{p\to\infty}\frac{D_{2p+2}}{D_{2p}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lim_{p\to\infty}\frac{D_{2p+2}}{D_{2p}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</syntaxhighlight> || <math>\nu \neq 2n+3, \nu = 2n+3, m > n</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">limit((D[2*p + 2])/(D[2*p]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Limit[Divide[Subscript[D, 2*p + 2],Subscript[D, 2*p]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/29.6.E59 29.6.E59] || <math qid="Q8693">\lim_{p\to\infty}\frac{D_{2p+2}}{D_{2p}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lim_{p\to\infty}\frac{D_{2p+2}}{D_{2p}} = \frac{k^{2}}{(1+k^{\prime})^{2}}</syntaxhighlight> || <math>\nu \neq 2n+3, \nu = 2n+3, m > n</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">limit((D[2*p + 2])/(D[2*p]), p = infinity) = ((k)^(2))/((1 +sqrt(1 - (k)^(2)))^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Limit[Divide[Subscript[D, 2*p + 2],Subscript[D, 2*p]], p -> Infinity, GenerateConditions->None] == Divide[(k)^(2),(1 +Sqrt[1 - (k)^(2)])^(2)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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29.6: Difference between revisions

Latest revision as of 12:09, 28 June 2021

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