On the differential equations associated with Srivastava's triple hypergeometric function \(H_C\) (Q2710530)

The triple hypergeometric function NEWLINE\[NEWLINEH_c=F_{16a}= \sum_{m,n,p} {(a)_{m+n} (b)_{n+p}(c)_{p+m} \over(f)_{m+n+p}} {x^my^nz^p \over m!n!p!}NEWLINE\]NEWLINE is a solution to a system of partial differential equations near the origin. It is shown how the properties of the Gauss function, \(_2F_1\) and its behavior in the neighborhoods of its singularities, along with the symmetries of \(H_c\), provides solutions near the other singularities of the partial differential equations. The methods involve only the use of elementary manipulations of series.