DLMF:29.5.E5 (Q8623): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:29.5.E5	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle{\lim_{k\to 1-}\frac{\mathit{Ec}^{m}_{\nu}\left(z,% k^{2}\right)}{\mathit{Ec}^{m}_{\nu}\left(0,k^{2}\right)}=\lim_{k\to 1-}\frac{% \mathit{Es}^{m+1}_{\nu}\left(z,k^{2}\right)}{\mathit{Es}^{m+1}_{\nu}\left(0,k^% {2}\right)}}=\frac{1}{(\cosh z)^{\mu}}F\left({\tfrac{1}{2}\mu-\tfrac{1}{2}\nu,% \tfrac{1}{2}\mu+\tfrac{1}{2}\nu+\tfrac{1}{2}\atop\tfrac{1}{2}};{\tanh^{2}}z% \right),}}

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DLMF:29.5.E5

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{\displaystyle{\displaystyle m}}

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$$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function

Defining formula

{\displaystyle{\displaystyle F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}

C15.S2.E1.m2adec

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Defining formula

{\displaystyle{\displaystyle\mathit{Ec}^{\NVar{m}}_{\NVar{\nu}}\left(\NVar{z},% \NVar{k^{2}}\right)}}

C29.S3.SS4.p1.m5abdec

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Defining formula

{\displaystyle{\displaystyle\mathit{Es}^{\NVar{m}}_{\NVar{\nu}}\left(\NVar{z},% \NVar{k^{2}}\right)}}

C29.S3.SS4.p1.m6aadec

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hyperbolic cosine function

Defining formula

{\displaystyle{\displaystyle\cosh\NVar{z}}}

C4.S28.E2.m2adec

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hyperbolic tangent function

Defining formula

{\displaystyle{\displaystyle\tanh\NVar{z}}}

C4.S28.E4.m2adec

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Defining formula

{\displaystyle{\displaystyle m}}

C29.S1.XMD1.m1cdec

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