A class of generalized hypergeometric summations

[摘要] Summations over the positive integers n of the generalized hypergeometric expressions (+/-1)F-n(p)p+1[-n(2)x(2)] (x > 0) are derived in closed form. The specialization p = 0, for example, reduces to known results for Schlomilch series. In addition, we record the apparently not readily available sine and cosine transforms of F-p(p+1)[-b(2)x(2)] (b > 0), the latter of which is used together with a form of the Poisson summation formula to deduce the aforementioned results.

[发布日期] 1997-12-18

[关键词] series of generalized hypergeometric functions;sine and cosine transforms