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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Main Authors: Gradimir V. Milovanović, Arjun K. Rathie, Nevena M. Vasović
Format: Article
Language:English
Published: Elsevier 2023-07-01
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.
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publishDate 2023-07-01
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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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