On Two Summation Formulas for the Generalized Hypergeometric Functions 3F2(1) and 4F3(1)

In this paper, we derive two new summation formulas for the generalized hypergeometric functions 4F3(1) and 3F2(1) by applying the generalizations of Kummer's second summation theorem for 2F1(1/2) to a known transformational formula of the generalized hypergeometric function 4F3(x) recorded in...

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Published in:General Letters in Mathematics Vol. 15; no. 2; pp. 42 - 48
Main Authors: Atash, Ahmed Ali, Bellehaj, Hussein Saleh
Format: Journal Article
Language:English
Published: 01.06.2025
ISSN:2519-9269, 2519-9277
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Abstract In this paper, we derive two new summation formulas for the generalized hypergeometric functions 4F3(1) and 3F2(1) by applying the generalizations of Kummer's second summation theorem for 2F1(1/2) to a known transformational formula of the generalized hypergeometric function 4F3(x) recorded in the book of Rainville. Further, we apply these results to evaluate some specific forms of 4F3(1) and 3F2(1). Our results are derived with the help of binomial theorem and certain properties of gamma function.
AbstractList In this paper, we derive two new summation formulas for the generalized hypergeometric functions 4F3(1) and 3F2(1) by applying the generalizations of Kummer's second summation theorem for 2F1(1/2) to a known transformational formula of the generalized hypergeometric function 4F3(x) recorded in the book of Rainville. Further, we apply these results to evaluate some specific forms of 4F3(1) and 3F2(1). Our results are derived with the help of binomial theorem and certain properties of gamma function.
Author Atash, Ahmed Ali
Bellehaj, Hussein Saleh
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Snippet In this paper, we derive two new summation formulas for the generalized hypergeometric functions 4F3(1) and 3F2(1) by applying the generalizations of Kummer's...
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Title On Two Summation Formulas for the Generalized Hypergeometric Functions 3F2(1) and 4F3(1)
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