Good morning, I need help with the following integral $$ \int_0 ^1 \left(\log (y) \frac{y^{a -1} {}_2F_1(a ,a ;2 a ;y)}{y-x} - \log (x) \frac{x^2 y^{a -3} {}_2F_1(a ,a ;2 a;y)}{y-x}\right) dy$$ where ${}_2F_1(a ,a ;2 a ;y)$ is the Gauss hypergeometric function, $a>0$ and $0<x<1$. I am looking for a result in terms of multivariate hypergeometric functions (Horn, Kampè de Feriet, Lauricella etc), if a simpler results does not exist. I tried expanding in series or using an integral representation for the hypergeometric function. Can anyone help me?
2026-03-30 16:41:45.1774888905
Integral of hypergeometric function
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