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Some results for generalized hypergeometric functions. (English) Zbl 0216.10701

In this paper the authors have summed up certain infinite series involving product of (1) \(H\)-function and, hypergeometric function \(_4F_3\), (ii) \(H\)-function and \(_6F_5\), (iii) Appell’s function \(F_4\) and Lauricella’s hypergeometric function \(F_0\), and (iv) confluent hypergeometric function \(\Psi_2\) and \(F_4\), respectively. The results obtained in this paper are general in nature and include as particular cases some of the results recently given by P. N. Rathie [Some series involving hypergeometric functions, Vijnana Parishad Anusandhan Patrika 11, 65–89 (1968); Nieuw Arch. Wiskd. III. Ser. 14, 261–267 (1966; Zbl 0145.07401); Port. Math. 26, 175–184 (1967; Zbl 0172.35301)]. A number of particular cases involving Wright’s generalized hypergeometric function \(_p\Psi_q\), Meijer’s \(G\)-function, Gauss’s hypergeometric function \(_2F_1\) etc. have been given.
Reviewer: P. N. Rathie

MSC:

33C20 Generalized hypergeometric series, \({}_pF_q\)
33C65 Appell, Horn and Lauricella functions
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