Summation identities for the Kummer confluent hypergeometric function 1F1(a; b;z)
The role which hypergeometric functions have in the numerical and symbolic calculation, especially in the fields of applied mathematics and mathematical physics motivated research in this paper. In this note, a general formula for the sum, with the Kummer confluent hypergeometric function 1F1(a; b;...
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| Format: | Article |
| Language: | English |
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Elsevier
2023-07-01
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| Series: | Kuwait Journal of Science |
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| Online Access: | https://www.sciencedirect.com/science/article/pii/S2307410823000688 |
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| author | Gradimir V. Milovanović Arjun K. Rathie Nevena M. Vasović |
| author_facet | Gradimir V. Milovanović Arjun K. Rathie Nevena M. Vasović |
| author_sort | Gradimir V. Milovanović |
| collection | DOAJ |
| description | The role which hypergeometric functions have in the numerical and symbolic calculation, especially in the fields of applied mathematics and mathematical physics motivated research in this paper. In this note, a general formula for the sum, with the Kummer confluent hypergeometric function 1F1(a; b; z) is derived and given in terms of the function 2F2(a; b; z). The idea for this investigation comes from the theory of generalized Gauss-Rys quadrature formulas developed recently by (Milovanović, 2018, Milovanović et al., 2018) and (Milovanović and Vasović, 2022). Several results are obtained as special cases of the main result. |
| format | Article |
| id | doaj-art-dc2d0c89bc4d43e9982379f202f0281d |
| institution | DOAJ |
| issn | 2307-4116 |
| language | English |
| publishDate | 2023-07-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Kuwait Journal of Science |
| spelling | doaj-art-dc2d0c89bc4d43e9982379f202f0281d2025-08-20T03:16:47ZengElsevierKuwait Journal of Science2307-41162023-07-01503190193https://doi.org/10.1016/j.kjs.2023.05.014Summation identities for the Kummer confluent hypergeometric function 1F1(a; b;z)Gradimir V. Milovanović0Arjun K. Rathie1Nevena M. Vasović2Serbian Academy of Sciences and Arts, 11000, Beograd, Serbia; University of Niš, Faculty of Sciences and Mathematics, 18000, Niš, Serbia; Dept. of Mathematics, Vedant College of Engineering & Technology, Rajastan Technical University, TULSI, Bundi, 323021, IndiaUniversity of Kragujevac, Faculty of Hotel Management and Tourism, 36210, Vrnjačka Banja, SerbiaThe role which hypergeometric functions have in the numerical and symbolic calculation, especially in the fields of applied mathematics and mathematical physics motivated research in this paper. In this note, a general formula for the sum, with the Kummer confluent hypergeometric function 1F1(a; b; z) is derived and given in terms of the function 2F2(a; b; z). The idea for this investigation comes from the theory of generalized Gauss-Rys quadrature formulas developed recently by (Milovanović, 2018, Milovanović et al., 2018) and (Milovanović and Vasović, 2022). Several results are obtained as special cases of the main result.https://www.sciencedirect.com/science/article/pii/S2307410823000688gegenbauer polynomialkummer confluent hypergeometric functionlegendre duplication formulaorthogonal polynomialssummation identities |
| spellingShingle | Gradimir V. Milovanović Arjun K. Rathie Nevena M. Vasović Summation identities for the Kummer confluent hypergeometric function 1F1(a; b;z) Kuwait Journal of Science gegenbauer polynomial kummer confluent hypergeometric function legendre duplication formula orthogonal polynomials summation identities |
| title | Summation identities for the Kummer confluent hypergeometric function 1F1(a; b;z) |
| title_full | Summation identities for the Kummer confluent hypergeometric function 1F1(a; b;z) |
| title_fullStr | Summation identities for the Kummer confluent hypergeometric function 1F1(a; b;z) |
| title_full_unstemmed | Summation identities for the Kummer confluent hypergeometric function 1F1(a; b;z) |
| title_short | Summation identities for the Kummer confluent hypergeometric function 1F1(a; b;z) |
| title_sort | summation identities for the kummer confluent hypergeometric function 1f1 a b z |
| topic | gegenbauer polynomial kummer confluent hypergeometric function legendre duplication formula orthogonal polynomials summation identities |
| url | https://www.sciencedirect.com/science/article/pii/S2307410823000688 |
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