65 research outputs found
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
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