Formula:7215

Digital Library of Mathematical Functions ID 19.25.E15

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \incellintPik@{\phi}{\alpha^{2}}{k}=\Carlsonmultivarhyper{-\frac{1}{2}}@{\tfrac{1}{2},\tfrac{1}{2},-\tfrac{1}{2},1}{c-1,c-k^{2},c,c-\alpha^{2}}.}

Symbols List

• ${\displaystyle{\displaystyle R_{\NVar{-a}}\left(\NVar{b_{1}},\dots,\NVar{b_{n}};\NVar{z_{1}},\dots,\NVar{z_{n}}\right)}}$: multivariate hypergeometric function
• ${\displaystyle{\displaystyle\Pi\left(\NVar{\phi},\NVar{\alpha}^{2},\NVar{k}\right)}}$: Legendre’s incomplete elliptic integral of the third kind
• ${\displaystyle{\displaystyle\phi}}$: real or complex argument
• ${\displaystyle{\displaystyle k}}$: real or complex modulus
• ${\displaystyle{\displaystyle\alpha^{2}}}$: real or complex parameter
 

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