DLMF:19.25.E22 (Q6526)

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Language	Label	Description	Also known as
English	DLMF:19.25.E22	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\mathrm{el3}\left(x,k_{c},p\right)=\mathrm{el1}% \left(x,k_{c}\right)+\tfrac{1}{3}{(1-p)}R_{J}\left(r,r+k_{c}^{2},r+1,r+p\right% ).}}

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DLMF:19.25.E22

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Defining formula

{\displaystyle{\displaystyle\mathrm{el1}\left(\NVar{x},\NVar{k_{c}}\right)}}

C19.S2.E15.m1abdec

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Bulirsch’s incomplete elliptic integral of the third kind

Defining formula

{\displaystyle{\displaystyle\mathrm{el3}\left(\NVar{x},\NVar{k_{c}},\NVar{p}% \right)}}

C19.S2.E16.m2adec

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symmetric elliptic integral of third kind

Defining formula

{\displaystyle{\displaystyle R_{J}\left(\NVar{x},\NVar{y},\NVar{z},\NVar{p}% \right)}}

C19.S16.E2.m2aedec

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Defining formula

{\displaystyle{\displaystyle k}}

C19.S1.XMD5.m1udec

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