Summation of some infinite series by the methods of Hypergeometric functions and partial fractions
| Autor: | M.I. Qureshi, J. Majid, A.H. Bhat |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Қарағанды университетінің хабаршысы. Математика сериясы, Vol 103, Iss 3, Pp 87-95 (2021) |
| Druh dokumentu: | article |
| ISSN: | 2518-7929 2663-5011 |
| DOI: | 10.31489/2021M3/87-95 |
| Popis: | In this article we obtain the summations of some infinite series by partial fraction method and by using certain hypergeometric summation theorems of positive and negative unit arguments, Riemann Zeta functions, polygamma functions, lower case beta functions of one-variable and other associated functions. We also obtain some hypergeometric summation theorems for: 8F7[9/2, 3/2, 3/2, 3/2, 3/2, 3, 3, 1; 7/2, 7/2, 7/2, 7/2, 1/2, 2, 2; 1], 5F4[5/3, 4/3, 4/3, 1/3, 1/3; 2/3, 1, 2, 2; 1], 5F4[9/4, 5/2, 3/2, 1/2, 1/2; 5/4, 2, 3, 3; 1], 5F4[13/8, 5/4, 5/4, 1/4, 1/4; 5/8, 2, 2, 1; 1], 5F4[1/2, 1/2, 5/2, 5/2, 1; 3/2, 3/2, 7/2, 7/2; −1], 4F3[3/2, 3/2, 1, 1; 5/2, 5/2, 2; 1], 4F3[2/3, 1/3, 1, 1; 7/3, 5/3, 2; 1], 4F3[7/6, 5/6, 1, 1; 13/6, 11/6, 2; 1] and 4F3[1, 1, 1, 1; 3, 3, 3; −1]. |
| Databáze: | Directory of Open Access Journals |
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