Simple connections between generalized hypergeometric series and dilogarithms (Q1375453)

A closed-form expression of a special Appell function of the third kind is deduced in the form of a linear combination of three dilogarithms. This result is obtained by considering an Euler integral representation of \(F_3\) with an integrand consisting of the product of two Gauss hypergeometric functions. The main result of this paper is interesting in that an \(F_3\) is involved in which its parameters are specialised while its two variables are unspecified. This work is in part motivated by considering certain Feynman integrals.