Appell series

Summary

The Appell series $F_1, F_2, F_3, F_4$ are four double power series in two variables $x$ and $y$ that generalise the Gauss hypergeometric series. Their coefficients are ratios of Pochhammer symbols in the two summation indices. Each of them reduces to a Gauss hypergeometric function when one of the variables is $0$. They appear in integrals of products of powers, in the theory of algebraic curves and in physics.