DLMF:19.8.E20 (Q6238)

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Language	Label	Description	Also known as
English	DLMF:19.8.E20	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\rho\Pi\left(\phi,\alpha^{2},k\right)=\frac{4}{1+k% ^{\prime}}\Pi\left(\psi_{1},\alpha_{1}^{2},k_{1}\right)+(\rho-1)F\left(\phi,k% \right)-R_{C}\left(c-1,c-\alpha^{2}\right),}}

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DLMF:19.8.E20

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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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Legendre’s incomplete elliptic integral of the first kind

Defining formula

{\displaystyle{\displaystyle F\left(\NVar{\phi},\NVar{k}\right)}}

C19.S2.E4.m2addec

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Legendre’s incomplete elliptic integral of the third kind

Defining formula

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

C19.S2.E7.m2aadec

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Defining formula

{\displaystyle{\displaystyle\phi}}

C19.S1.XMD4.m1gdec

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Defining formula

{\displaystyle{\displaystyle k}}

C19.S1.XMD5.m1ndec

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Defining formula

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

C19.S1.XMD6.m1kdec

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Defining formula

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

C19.S1.XMD7.m1edec

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Defining formula

{\displaystyle{\displaystyle k_{1}}}

C19.S8.XMD13.m1bdec

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Defining formula

{\displaystyle{\displaystyle\psi_{1}}}

C19.S8.XMD14.m1bdec

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Defining formula

{\displaystyle{\displaystyle\rho}}

C19.S8.XMD16.m1dec

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Defining formula

{\displaystyle{\displaystyle\alpha_{1}^{2}}}

C19.S8.XMD17.m1dec

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Defining formula

{\displaystyle{\displaystyle c}}

C19.S8.XMD18.m1dec

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Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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