SOME SUMMATION FORMULAS FOR THE HYPERGEOMETRIC SERIES

Amaç & Hipotez:The aim of this paper is to obtain explicit expressions of the generalizedhypergeometric function r+2Fr+1a, b, 1 2 (a + b + j + 1), (fr + mr) (fr) ; 1 2 for j = 0, ±1, . . . , ±5, where r pairs of numeratorial and denominatorialparameters differ by positive integers mr.

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Temel Bulgular & Veri:The results are derived withthe help of an expansion in terms of a finite sum of 2F1( 1 2 ) functions anda generalization of Gauss' second summation theorem due to Lavoie etal. [J.

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Sonuç & Katkı:Some special andlimiting cases are also given.

🔬Tür:Araştırma Makalesi

📍Kapsam:Genişletilmiş Akademik Örneklem

⚙️Değişkenler:Alan Parametreleri

Abstract

The aim of this paper is to obtain explicit expressions of the generalizedhypergeometric function r+2Fr+1a, b, 1 2 (a + b + j + 1), (fr + mr) (fr) ; 1 2 for j = 0, ±1, . . . , ±5, where r pairs of numeratorial and denominatorialparameters differ by positive integers mr. The results are derived withthe help of an expansion in terms of a finite sum of 2F1( 1 2 ) functions anda generalization of Gauss' second summation theorem due to Lavoie etal. [J. Comput. Appl. Math. 72, 293-300 (1996)]. Some special andlimiting cases are also given.

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Bu Makaleye Atıf Yap

KİM, Y. S., RATHİE, A. K., PARİS, R. B., PANDEY, U. (2022). SOME SUMMATION FORMULAS FOR THE HYPERGEOMETRIC SERIES. Hacettepe Journal of Mathematics and Statistics, Cilt: 42 - Sayı: 3, 3542–6960. https://ajindex.com/articles/530402

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Kaynakça (16)

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