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Keywords = Bailey quadratic transformation

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26 pages, 465 KB  
Article
Three General Double-Series Identities and Associated Reduction Formulas and Fractional Calculus
by Mohd Idris Qureshi, Tafaz Ul Rahman Shah, Junesang Choi and Aarif Hussain Bhat
Fractal Fract. 2023, 7(10), 700; https://doi.org/10.3390/fractalfract7100700 - 23 Sep 2023
Cited by 3 | Viewed by 1392
Abstract
In this article, we introduce three general double-series identities using Whipple transformations for terminating generalized hypergeometric 4F3 and 5F4 functions. Then, by employing the left-sided Riemann–Liouville fractional integral on these identities, we show the ability to derive additional identities [...] Read more.
In this article, we introduce three general double-series identities using Whipple transformations for terminating generalized hypergeometric 4F3 and 5F4 functions. Then, by employing the left-sided Riemann–Liouville fractional integral on these identities, we show the ability to derive additional identities of the same nature successively. These identities are used to derive transformation formulas between the Srivastava–Daoust double hypergeometric function (S–D function) and Kampé de Fériet’s double hypergeometric function (KDF function) with equal arguments. We also demonstrate reduction formulas from the S–D function or KDF function to the generalized hypergeometric function pFq. Additionally, we provide general summation formulas for the pFq and S–D function (or KDF function) with specific arguments. We further highlight the connections between the results presented here and existing identities. Full article
(This article belongs to the Special Issue Fractional Calculus and Hypergeometric Functions in Complex Analysis)
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