The Confluent Hypergeometric Function

The routines S22BA and S22BB, new at Mark 24, provide the functionality to calculate the confluent hypergeometric function 1F1(a; b; x), also known as Kummer’s function M(a, b, x). This has a wide variety of applications, including CIR processes and pricing Asian options. Many special functions are also expressible as special cases of 1F1, including the incomplete gamma function, Bessel functions and Laguerre polynomials. M(a, b, x) is one of the independent solutions to the differential equation,