Summation of some infinite series by the methods of Hypergeometric functions and partial fractions
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 associ...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Academician Ye.A. Buketov Karaganda University
2021-09-01
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| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
| Online Access: | https://mathematics-vestnik.ksu.kz/apart/2021-103-3/9.pdf |
| _version_ | 1797686713049415680 |
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| author | M.I. Qureshi J. Majid A.H. Bhat |
| author_facet | M.I. Qureshi J. Majid A.H. Bhat |
| author_sort | M.I. Qureshi |
| collection | DOAJ |
| description | 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]. |
| first_indexed | 2024-03-12T01:09:48Z |
| format | Article |
| id | doaj.art-67d078f41e78491fac8a19a4929e64bb |
| institution | Directory Open Access Journal |
| issn | 2518-7929 2663-5011 |
| language | English |
| last_indexed | 2024-03-12T01:09:48Z |
| publishDate | 2021-09-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj.art-67d078f41e78491fac8a19a4929e64bb2023-09-14T06:33:42ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112021-09-011033879510.31489/2021M3/87-95Summation of some infinite series by the methods of Hypergeometric functions and partial fractionsM.I. QureshiJ. MajidA.H. Bhat 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].https://mathematics-vestnik.ksu.kz/apart/2021-103-3/9.pdf |
| spellingShingle | M.I. Qureshi J. Majid A.H. Bhat Summation of some infinite series by the methods of Hypergeometric functions and partial fractions Қарағанды университетінің хабаршысы. Математика сериясы |
| title | Summation of some infinite series by the methods of Hypergeometric functions and partial fractions |
| title_full | Summation of some infinite series by the methods of Hypergeometric functions and partial fractions |
| title_fullStr | Summation of some infinite series by the methods of Hypergeometric functions and partial fractions |
| title_full_unstemmed | Summation of some infinite series by the methods of Hypergeometric functions and partial fractions |
| title_short | Summation of some infinite series by the methods of Hypergeometric functions and partial fractions |
| title_sort | summation of some infinite series by the methods of hypergeometric functions and partial fractions |
| url | https://mathematics-vestnik.ksu.kz/apart/2021-103-3/9.pdf |
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