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SOME MODIFIED REDUCTION FORMULAS FOR THE GAUSS AND CLAUSEN HYPERGEOMETRIC FUNCTIONS

H. M. Srivastava|M. I. QURESHI|SHAKIR HUSSAIN MALIK
장전수학회 (Jangjeon Mathematical Society)|2021.07|Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집) (Proceedings of the Jangjeon Mathematical Society)|제24권 제3호|pp. 275-283|DOI 10.17777/pjms.2021.24.3.002

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키워드

Hypergeometric transformationsSummationtransformation and reduction formulasGauss and Clausen hypergeometric functions
주제분류수학

초록

In this paper, by using the series rearrangement technique, we derive closed forms of some reduction formulas for the following two Clausen hypergeo- metric functions: and. We also obtain some reduction formulas of the following four Gauss hypergeometric functions: and. Several appropriately modi ed forms of a known reduction formula for the Clausen hypergeometric function are also appropriately derived here.

Abstract

In this paper, by using the series rearrangement technique, we derive closed forms of some reduction formulas for the following two Clausen hypergeo- metric functions: and. We also obtain some reduction formulas of the following four Gauss hypergeometric functions: and. Several appropriately modi ed forms of a known reduction formula for the Clausen hypergeometric function are also appropriately derived here.

참고문헌 (18)

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  9. G. V. Milovanovic, "Four unified results for reducibility of Srivastava's triple yypergeometric series HB", Montes Taurus J. Pure Appl. Math, 3, pp.1~10 (2021)
  10. E. D. Rainville, "Special Functions" (1971), Chelsea Publishing Company
  11. L. J. Slater, "Generalized Hypergeometric Functions" (1966), Cambridge University Press
  12. H. M. Srivastava, "Some families of generating functions and associated hypergeometric transformation and reduction formulas", Russian J. Math. Phys, 23, pp.382~391 (2016)
  13. H. M. Srivastava, "Multiple Gaussian Hypergeometric Series" (1985), Halsted Press, John Wiley and Sons
  14. H. M. Srivastava, "A Treatise on Generating Functions" (1984), Halsted Press, John Wiley and Sons
  15. H. M. Srivastava, "Some general series identities and summation theorems for the Gauss hypergeometric function with negative integer numerator and denominator parameters", J. Nonlinear Convex Anal, 21, pp.463~478 (2020)
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  18. H. M. Srivastava, "Extensions of the classical theorems for very wellpoised hypergeometric functions", Rev. Real Acad. Cienc. Exactas Fs. Natur. Ser. A Mat. (RAC-SAM), 113, pp.367~397 (2019)

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