Summation identities for the Kummer confluent hypergeometric function 1F1(a; b;z)

Abstract

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.

Keywords

• gegenbauer polynomial
• kummer confluent hypergeometric function
• legendre duplication formula
• orthogonal polynomials
• summation identities