Computation of the confluent hypergeometric function

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 ∼ 1 0 − 14 relative accuracy in the parameter region ( a , b , x ) ∈ (0,500) × (0,500) × (0,1000) in double-precision floating point arithmetic.