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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Some of them are lifted up, via a trigonometric integral approach, to identities of nonterminating $_3F_2$-series.
📌 3 Key Takeaways
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Objective & Hypothesis:The classical Gaussian $_2F_1$-series containing two free variables $\{x,y\}$ and two integer parameters $\{m,n\}$ are investigated by the linearization method.
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Key Findings & Data:Several closed formulae are derived in terms of trigonometric functions.
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Conclusion & Impact:Some of them are lifted up, via a trigonometric integral approach, to identities of nonterminating $_3F_2$-series.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Classical hypergeometric series · Pfaff-Saalsch summation theorem · linearization method
Abstract
The classical Gaussian $_2F_1$-series containing two free variables $\{x,y\}$ and two integer parameters $\{m,n\}$ are investigated by the linearization method. Several closed formulae are derived in terms of trigonometric functions. Some of them are lifted up, via a trigonometric integral approach, to identities of nonterminating $_3F_2$-series.
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Cite This Article
CHU, W. (2019). Trigonometric expressions for Gaussian $_2F_1$-series. Turkish Journal of Mathematics, Cilt: 43 - Sayı: 4, 1823–1836. https://ajindex.com/articles/208970