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

On extensions of two results due to Ramanujan

Yong Sup KIM
Arjunkumar RATHIE
Rıchard B. PARIS
Pages
348–355
Publication Date
2020-03-01
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 include integral 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 that relate sums involving the derivatives of a function $\varphi\left t\right $ evaluated at 0 and 1.
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Key Findings & Data:The generalization obtained is derived with the help of expressions for the sum of terminating ${}_3F_2$ hypergeometric functions of argument equal to 2, recently obtained by Kim et. al. [Two results for the terminating ${}_3F_2$ 2 with applications, Bulletin of the Korean Mathematical Society 2012; 49: 621-633].
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Conclusion & Impact:In addition we generalize a summation formula to include integral parameter differences.
🔬Design:Research Article
📍Scope:2012 Verileri
⚙️Variables:Hypergeometric series · Ramanujan's sum · sums of Hermite polynomials

Abstract

The aim in this note is to provide a generalization of an interesting entry in Ramanujan's notebooks that relate sums involving the derivatives of a function $\varphi\left t\right $ evaluated at 0 and 1. The generalization obtained is derived with the help of expressions for the sum of terminating ${}_3F_2$ hypergeometric functions of argument equal to 2, recently obtained by Kim et. al. [Two results for the terminating ${}_3F_2$ 2 with applications, Bulletin of the Korean Mathematical Society 2012; 49: 621-633]. Several special cases are given. In addition we generalize a summation formula to include integral parameter differences.

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Cite This Article

KIM, Y. S., RATHIE, A., PARIS, R. B. (2020). On extensions of two results due to Ramanujan. Turkish Journal of Mathematics, Cilt: 44 - Sayı: 2, 348–355. https://ajindex.com/articles/185518

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References (10)

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