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; 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.