The Kampé de Fériet functions: A family of reduction formulae (Q1341111)

The authors consider Kampé de Fériet series \(F_{q:n;0}^{p:m;1}\) for which the numerator parameter associated with the second variable is equal to 1. They show that such a series may be written as a single series whose general term involves a truncated \({}_ m F_ n\). Known formulae for the latter then lead to the reduction formulae for \(F_{q:n;0}^{p:m;1}\). Apart from one case, \(m\) equals \(n+1\).