Lauricella hypergeometric series

In 1893 Giuseppe Lauricella defined and studied four hypergeometric series FA, FB, FC, FD of three variables. They are (Lauricella 1893): F A ( 3 ) ( a , b 1 , b 2 , b 3 , c 1 , c 2 , c 3 ; x 1 , x 2 , x 3 ) = ∑ i 1 , i 2 , i 3 = 0 ∞ ( a ) i 1 + i 2 + i 3 ( b 1 ) i 1 ( b 2 ) i 2 ( b 3 ) i 3 ( c 1 ) i 1 ( c 2 ) i 2 ( c 3 ) i 3 i 1 !

Source: Wikipedia — Lauricella hypergeometric series (CC BY-SA 4.0)