DLMF:29.5.E6 (Q8624)

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Language	Label	Description	Also known as
English	DLMF:29.5.E6	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\lim_{k\to 1-}\frac{\mathit{Ec}^{m}_{\nu}\left(z,k% ^{2}\right)}{\left.\ifrac{\mathrm{d}\mathit{Ec}^{m}_{\nu}\left(z,k^{2}\right)}% {\mathrm{d}z}\right|_{z=0}}=\lim_{k\to 1-}\frac{\mathit{Es}^{m+1}_{\nu}\left(z% ,k^{2}\right)}{\left.\ifrac{\mathrm{d}\mathit{Es}^{m+1}_{\nu}\left(z,k^{2}% \right)}{\mathrm{d}z}\right|_{z=0}}=\frac{\tanh z}{(\cosh z)^{\mu}}F\left({% \tfrac{1}{2}\mu-\tfrac{1}{2}\nu+\tfrac{1}{2},\tfrac{1}{2}\mu+\tfrac{1}{2}\nu+1% \atop\tfrac{3}{2}};{\tanh^{2}}z\right),}}

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DLMF:29.5.E6

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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.m2aadec

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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.m5acdec

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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.m6abdec

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derivative of $$f$$ with respect to $$x$$

Defining formula

{\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}

C1.S4.E4.m2adec

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hyperbolic cosine function

Defining formula

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

C4.S28.E2.m2aadec

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hyperbolic tangent function

Defining formula

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

C4.S28.E4.m2aadec

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Defining formula

{\displaystyle{\displaystyle m}}

C29.S1.XMD1.m1ddec

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