DLMF:19.21.E5 (Q6423)

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Language	Label	Description	Also known as
English	DLMF:19.21.E5	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle 2R_{G}\left(0,z-1,z\right)=2R_{G}\left(0,1-z,1% \right)\pm\mathrm{i}2R_{G}\left(0,z,1\right)+(z-1)R_{F}\left(0,1-z,1\right)\mp% \mathrm{i}zR_{F}\left(0,z,1\right).}}

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DLMF:19.21.E5

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symmetric elliptic integral of first kind

Defining formula

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

C19.S16.E1.m2addec

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symmetric elliptic integral of second kind

Defining formula

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

C19.S16.E3.m2aadec

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Defining formula

{\displaystyle{\displaystyle\mathrm{i}}}

C1.S9.E1.m2aadec

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