Computation of the confluent hypergeometric function U(a,b,x) and its derivative for positive arguments

Abstract

An algorithm and a MATLAB implementation for computing the Kummer function U(a,b,x) and its derivative is given in this paper. The algorithm is efficient and accurate. Numerical tests show that the MATLAB algorithm allows the computation of the function with sim 10^{-14} relative accuracy in the parameter region (a,b,x) ∈ (0,500) × (0,500) × (0,1000) in double-precision floating point arithmetic.