DLMF:19.12.E4 (Q6302)

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Language	Label	Description	Also known as
English	DLMF:19.12.E4	No description defined

Statements

Defining formula

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

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DLMF:19.12.E4

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

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order not exceeding

Defining formula

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

C2.S1.E3.m2adec

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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.m2adec

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Defining formula

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

C19.S2.E8.m4adec

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principal branch of logarithm function

Defining formula

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

C4.S2.E2.m2abdec

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Defining formula

{\displaystyle{\displaystyle k}}

C19.S1.XMD5.m1bdec

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Defining formula

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

C19.S1.XMD6.m1bdec

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Defining formula

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

C19.S1.XMD7.m1dec

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