A note on the summation of an infinite series involving a hypergeometric function
نویسنده
چکیده
The mathematical properties of the generalized hypergeometric function are now well established, due largely to the efforts of Bailey, Watson, Slater, and many others. There are available a number of books on the subject ['], [6] which contain extensive bibliographies together with an outline of the history of the investigations. A large portion of the published work concerning these functions has in fact dealt with the Gauss hypergeometric function and, as a consequence, many interesting results have been documented. Such results include the evaluation of the function for special values of parameters and argument, asymptotic expansions and so on. The situation, in this regard, for other hypergeometric functions is not as satisfactory. The exception is Kummer's function which like the Gauss function has been well researched.
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