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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Bibliographic Details
Published inKuwait journal of science Vol. 50; no. 3; pp. 190 - 193
Main Authors Milovanović, Gradimir V., Rathie, Arjun K., Vasović, Nevena M.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.07.2023
Subjects
Gegenbauer polynomial
Kummer confluent hypergeometric function
Legendre duplication formula
Orthogonal polynomials
Summation identities
Kummer confluent hypergeometric function
Summation identities
Legendre duplication formula
Orthogonal polynomials
Gegenbauer polynomial
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Summary: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) and (Milovanović and Vasović, 2022). Several results are obtained as special cases of the main result.
ISSN:2307-4108
2307-4116
DOI:10.1016/j.kjs.2023.05.014