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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Two applications are considered, where the first summation formula is applied to a terminating $_3F_2(2)$ series and the confluent hypergeometric function $_1F_1(x)$.
📌 3 Key Takeaways
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Objective & Hypothesis:Explicit expressions for the hypergeometric series $_2F_1(-n, a; 2a\pm j;2)$ and $_2F_1(-n, a; -2n \pm j;2)$ for positive integer $n$ and arbitrary integer $j$ are obtained with the help of generalizations of Kummer's second and third summation theorems obtained earlier by Rakha and Rathie.
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Key Findings & Data:Results for $|j|\leq 5$ derived previously using different methods are also obtained as special cases.
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Conclusion & Impact:Two applications are considered, where the first summation formula is applied to a terminating $_3F_2(2)$ series and the confluent hypergeometric function $_1F_1(x)$.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Terminating hypergeometric series · generalized Kummer's second and third summation theorems
Abstract
Explicit expressions for the hypergeometric series $_2F_1(-n, a; 2a\pm j;2)$ and $_2F_1(-n, a; -2n \pm j;2)$ for positive integer $n$ and arbitrary integer $j$ are obtained with the help of generalizations of Kummer's second and third summation theorems obtained earlier by Rakha and Rathie. Results for $|j|\leq 5$ derived previously using different methods are also obtained as special cases. Two applications are considered, where the first summation formula is applied to a terminating $_3F_2(2)$ series and the confluent hypergeometric function $_1F_1(x)$.
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Cite This Article
KIM, Y. S., RATHIE, A., PARIS, R. B. (2018). Evaluations of some terminating hypergeometric $_2F_1(2)$ series with applications. Turkish Journal of Mathematics, Cilt: 42 - Sayı: 5, 2563–2575. https://ajindex.com/articles/723062