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Zbl 0903.33005
Miller, Allen R.
A class of generalized hypergeometric summations. (English)
[J] J. Comput. Appl. Math. 87, No.1, 79-85 (1997). ISSN 0377-0427

{\it A. R. Miller} [ibid. 80, No. 1, 83-95 (1997; Zbl 0870.33003)] had given closed form representations for two infinite hypergeometric sums which contain certain Schlömlich series and sums of Lommel and Struve functions. In this paper, values of $$C(a,b)= \int^\infty_0 \cos(2ax){_pF_{p+1}} [(\alpha_p); (\beta_{p+ 1}); -b^2x^2]dx$$ and $$S(a,b)= \int^\infty_0 \sin(2ax){_pF_{p+ 1}}[(\alpha_p); (\beta_{p+ 1}); -b^2x^2]dx,$$ under their convergence conditions, are first obtained and closed form representations for the sums $$\sum^\infty_{n= 1} (\pm 1)^n{_pF_{p+ 1}}[(\alpha_p); (\beta_{p+ 1}); -n^2x^2],$$ where $p$ is a nonnegative integer, together with conditions of their convergence, are given.
[K.M.Saksena (Kanpur)]

MSC 2000:: *33C20 Generalized hypergeometric series
44A20 Integral transforms of special functions

Keywords: Lommel function; cosine transforms; sine transform; Schlömlich series; Struve functions

Citations: Zbl 0870.33003

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