Formula:9716

Digital Library of Mathematical Functions ID 31.7.E1

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \genhyperF{2}{1}@{\alpha,\beta}{\gamma}{z}=\HeunHl@{1}{\alpha\beta}{\alpha}{\beta}{\gamma}{\delta}{z}=\HeunHl@{0}{0}{\alpha}{\beta}{\gamma}{\alpha+\beta+1-\gamma}{z}=\HeunHl@{a}{a\alpha\beta}{\alpha}{\beta}{\gamma}{\alpha+\beta+1-\gamma}{z}.}

Symbols List

• ${\displaystyle{\displaystyle{{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}$: = F ( a , b ; c ; z ) notation for Gauss’ hypergeometric function
• ${\displaystyle{\displaystyle\mathit{H\!\ell}\left(\NVar{a},\NVar{q};\NVar{\alpha},\NVar{\beta},\NVar{\gamma},\NVar{missing};missing\right)\)\@add@PDF@RDFa@triples\end{document}}}$: Heun functions
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\gamma}}$: real or complex parameter
• ${\displaystyle{\displaystyle\delta}}$: real or complex parameter
• ${\displaystyle{\displaystyle a}}$: complex parameter
• ${\displaystyle{\displaystyle\alpha}}$: real or complex parameter
• ${\displaystyle{\displaystyle\beta}}$: real or complex parameter
 

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