Making suitable adjustment of parameters in reduction formulas for 4F3 and 3F2 , we obtain some results in terms of elementary functions and some special functions like Lerch generalized zeta function and incomplete beta function.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, we obtain a general double-series identity involving the bounded sequence of arbitrary complex numbers.
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Key Findings & Data:As application of our double-series identity, we establish some reduction formulas for Srivastava–Daoust double hypergeometric function and Gaussian generalized hypergeometric function 4F3 .
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Conclusion & Impact:Making suitable adjustment of parameters in reduction formulas for 4F3 and 3F2 , we obtain some results in terms of elementary functions and some special functions like Lerch generalized zeta function and incomplete beta function.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
In this paper, we obtain a general double-series identity involving the bounded sequence of arbitrary complex numbers. As application of our double-series identity, we establish some reduction formulas for Srivastava–Daoust double hypergeometric function and Gaussian generalized hypergeometric function 4F3 . As special cases of our reduction formula for 4F3 lead to some corollaries involving Clausen hypergeometric functions 3F2 . Making suitable adjustment of parameters in reduction formulas for 4F3 and 3F2 , we obtain some results in terms of elementary functions and some special functions like Lerch generalized zeta function and incomplete beta function.
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Cite This Article
MALIK, S. H., QURESHI, M. I. (2022). A general double-series identity and its application in hypergeometric reduction formulas. Turkish Journal of Mathematics, Cilt: 45 - Sayı: 6, 2759–2772. https://ajindex.com/articles/607407
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