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 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
01.06.2025
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| ISSN: | 2519-9269, 2519-9277 |
| Online Access: | Get full text |
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| Summary: | 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. |
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| ISSN: | 2519-9269 2519-9277 |
| DOI: | 10.31559/glm2025.15.2.2 |