Formula:9753

Digital Library of Mathematical Functions ID 31.10.E10

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \mathcal{K}(z,t)=(zt-a)^{\frac{1}{2}-\delta-\sigma}\*\genhyperF{2}{1}@@{\frac{1}{2}-\delta-\sigma+\alpha,\frac{1}{2}-\delta-\sigma+\beta}{\gamma}{\frac{zt}{a}}\*\genhyperF{2}{1}@@{-\frac{1}{2}+\delta+\sigma,-\frac{1}{2}+\epsilon-\sigma}{\delta}{\frac{a(z-1)(t-1)}{(a-1)(zt-a)}},}

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
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\gamma}}$: real or complex parameter
• ${\displaystyle{\displaystyle\delta}}$: real or complex parameter
• ${\displaystyle{\displaystyle\epsilon}}$: real or complex parameter
• ${\displaystyle{\displaystyle a}}$: complex parameter
• ${\displaystyle{\displaystyle\alpha}}$: real or complex parameter
• ${\displaystyle{\displaystyle\beta}}$: real or complex parameter
• ${\displaystyle{\displaystyle\mathcal{K}(z,t)}}$: kernel (locally)
• ${\displaystyle{\displaystyle\sigma}}$: separation constant
 

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