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Journals / Turkish Journal of Mathematics / 2020 / Cilt: 44 - Sayı: 2

On extensions of two results due to Ramanujan

Richard Bruce PARIS
Arjun Kummar RATHIE
Yong Sup KIM
Pages
348–355
Publication Date
2022-11-04
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

In addition we generalize a summation formula to includeintegral parameter differences

📌 3 Key Takeaways

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Objective & Hypothesis:The aim in this note is to provide a generalization of an interesting entry in Ramanujan’s notebooks thatrelate sums involving the derivatives of a function φ(t) evaluated at 0 and 1.
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Key Findings & Data:The generalization obtained is derivedwith the help of expressions for the sum of terminating 3F2 hypergeometric functions of argument equal to 2, recentlyobtained by Kim et. al. [Two results for the terminating 3F2(2) with applications, Bulletin of the Korean MathematicalSociety 2012; 49: 621-633].
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Conclusion & Impact:In addition we generalize a summation formula to includeintegral parameter differences
🔬Design:Research Article
📍Scope:2012 Verileri
⚙️Variables:Domain Parameters

Abstract

The aim in this note is to provide a generalization of an interesting entry in Ramanujan’s notebooks thatrelate sums involving the derivatives of a function φ(t) evaluated at 0 and 1. The generalization obtained is derivedwith the help of expressions for the sum of terminating 3F2 hypergeometric functions of argument equal to 2, recentlyobtained by Kim et. al. [Two results for the terminating 3F2(2) with applications, Bulletin of the Korean MathematicalSociety 2012; 49: 621-633]. Several special cases are given. In addition we generalize a summation formula to includeintegral parameter differences

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Cite This Article

PARIS, R. B., RATHIE, A. K., KIM, Y. S. (2022). On extensions of two results due to Ramanujan. Turkish Journal of Mathematics, Cilt: 44 - Sayı: 2, 348–355. https://ajindex.com/articles/607542

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References (10)

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  4. Kim YS, Rathie AK, Paris RB. Generalization of two theorems due to Ramanujan. Integral Transforms and Special Functions 2012; 24: 314-323
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