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Journals / Hacettepe Journal of Mathematics and Statistics / 2011 / Cilt: 40 - Sayı: 6

TWO FORMULAS CONTIGUOUS TO A QUADRATIC TRANSFORMATION DUE TO KUMMER WITH AN APPLICATION

Junesang CHOİ
Arjun K. RATHİE
Pages
885–894
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

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

They are further applied to prove two summation formulas for the series 3F2(1), closely related to the classical Watson’s theorem due to Lavoie.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We aim at establishing two identities contiguous to Kummer’s transformation :(1 − z)−a2F1" 12a, 12a +12;b +12;z1 − z2#= 2F1a, b ;2b ;2zby using two different methods.
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Key Findings & Data:We aim at establishing two identities contiguous to Kummer’s transformation :(1 − z)−a2F1" 12a, 12a +12;b +12;z1 − z2#= 2F1a, b ;2b ;2zby using two different methods.
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Conclusion & Impact:They are further applied to prove two summation formulas for the series 3F2(1), closely related to the classical Watson’s theorem due to Lavoie.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Gamma function · Hypergeometric function · Generalized hypergeometric function

Abstract

We aim at establishing two identities contiguous to Kummer’s transformation :(1 − z)−a2F1" 12a, 12a +12;b +12;z1 − z2#= 2F1a, b ;2b ;2zby using two different methods. They are further applied to prove two summation formulas for the series 3F2(1), closely related to the classical Watson’s theorem due to Lavoie.

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Cite This Article

CHOİ, J., RATHİE, A. K. (2022). TWO FORMULAS CONTIGUOUS TO A QUADRATIC TRANSFORMATION DUE TO KUMMER WITH AN APPLICATION. Hacettepe Journal of Mathematics and Statistics, Cilt: 40 - Sayı: 6, 885–894. https://ajindex.com/articles/530548

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