DLMF:19.12.E5 (Q6303)

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Language	Label	Description	Also known as
English	DLMF:19.12.E5	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle(1-\alpha^{2})\Pi\left(\alpha^{2},k\right)=\left(% \ln\left(\frac{4}{k^{\prime}}\right)-R_{C}\left(1,1-\alpha^{-2}\right)\right)% \*\left(1+O\left({k^{\prime}}^{2}\right)\right),}}

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DLMF:19.12.E5

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{\displaystyle{\displaystyle 1<\alpha^{2}<\infty}}

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order not exceeding

Defining formula

{\displaystyle{\displaystyle O\left(\NVar{x}\right)}}

C2.S1.E3.m2aadec

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Carlson’s combination of inverse circular and inverse hyperbolic functions

Defining formula

{\displaystyle{\displaystyle R_{C}\left(\NVar{x},\NVar{y}\right)}}

C19.S2.E17.m2aadec

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Defining formula

{\displaystyle{\displaystyle\Pi\left(\NVar{\alpha}^{2},\NVar{k}\right)}}

C19.S2.E8.m4aadec

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principal branch of logarithm function

Defining formula

{\displaystyle{\displaystyle\ln\NVar{z}}}

C4.S2.E2.m2acdec

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Defining formula

{\displaystyle{\displaystyle k}}

C19.S1.XMD5.m1cdec

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Defining formula

{\displaystyle{\displaystyle k^{\prime}}}

C19.S1.XMD6.m1cdec

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Defining formula

{\displaystyle{\displaystyle\alpha^{2}}}

C19.S1.XMD7.m1adec

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