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 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

\pi and other formulae implied by hypergeometric summation theorems

By employing certain extended classical summation theorems, several surprising \pi and other formulae are displayed

Evaluations of some terminating hypergeometric ₂F₁(2) series with applications

Explicit expressions for the hypergeometric series 2F1(-n, a; 2a±j; 2) and 2F1(-n, a;-2n±j; 2) for positive integer n and arbitrary integer j are obtained with the help of generalizations of Kummer's second and third summation theorems obtained earlier by Rakha and Rathie. Results for |j| ≤ 5 derived previously using different methods are also obtained as special cases. Two applications are considered, where the first summation formula is applied to a terminating 3F2(2) series and the confluent hypergeometric function 1F1(x).</p