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

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 similar to 10(-14) relative accuracy in the parameter region (a, b, x) is an element of (0, 500) x (0, 500) x (0, 1000) in double-precision floating point arithmetic.

Automated summary

This paper presents an algorithm and MATLAB implementation for computing the Kummer function U(a, b, x) and its derivative. The algorithm is efficient and accurate. Numerical tests demonstrate that the MATLAB algorithm can compute the function with a relative accuracy of about 10^(-14) in the parameter region (a, b, x) ∈ (0, 500) × (0, 500) × (0, 1000) in double-precision floating point arithmetic.