Lauricella hypergeometric series

Summary

The Lauricella series $F_A^{(n)}, F_B^{(n)}, F_C^{(n)}, F_D^{(n)}$ are four multiple power series in $n$ variables that extend the Appell series from two variables to any number of variables. For $n = 2$ they are the Appell series $F_2, F_3, F_4, F_1$, and for $n = 1$ each becomes the Gauss hypergeometric series. The series $F_D$ is the most used: it has a one-dimensional Euler-type integral and it describes periods of certain algebraic curves.