A new proof of Watson's theorem for the series 3F2(1)

We give a new proof of the classical Watson theorem for the summation of a 3F2 hypergeometric series of unit argument. The proof relies on the two well-known Gauss summation theorems for the 2F1 function

A derivation of two transformation formulas contiguous to that of Kummer’s second theorem via a differential equation approach

The purpose of this note is to provide an alternative proof of two transformation formulas contiguous to that of Kummer’s second transformation for the confluent hypergeometric function 1F1 using a differential equation approach

A derivation of two quadratic transformations contiguous to that of Gauss via a differential equation approach

The purpose of this note is to provide an alternative proof of two quadratic transformation formulas contiguous to that of Gauss using a differential equation approach

An extension of Saalschütz's summation theorem for the series _<i>r</i>+3F_<i>r</i>+2

The aim in this research note is to provide an extension of Saalschütz's summation theorem for the series r+3Fr+2(1) when r pairs of numeratorial and denominatorial parameters differ by positive integers. The result is obtained by exploiting a generalization of an Euler-type transformation recently derived by Miller and Paris [Transformation formulas for the generalized hypergeometric function with integral parameter differences. Rocky Mountain J Math. 2013;43, to appear]