New transformation formulas for the fourth Lauricella function. II (Q6655821)

This work is part of a series of papers on multiple (\(q\)-)hypergeometric series where the authors consider different transformations on the fourth Lauricella function. They start considering Lauricella functions with \(m\) equal variables or with \(m\) copies of \(1\) that can be reduced to a similar function. Similarly, they show that Lauricella functions with \(m\) parameters equal to \(-1\) can be reduced to a sum of Lauricella functions times elementary symmetric polynomials of the variables. These formulae are used in the proofs and transformation formulae for Lauricella functions. Their method, using in most of the cases Eulerian (\(q\)-)integrals, provides a transformation with Kampé de Fériet functions and summation formulae for the first Appell function.