KUMMERCOMPLEX(a,b,z) is the confluent hypergeometric function 1F1 (Kummer function) for complex parameters a, b and complex variable z.
In general case the program calculates the sum of convergent series defining the function until the next term becomes too small (in comparison with the sum of all previous terms). The case of large abs(z) is considered separately (e.g., see 13.5.1 in Abramowitz, Stegun "Handbook of special functions", 1964). Some simple cases of integer parameter values are considered separately as well.
The function controls the loss of precision and makes check for insufficient number of members in the series. It prints warning if there are any problems. Otherwise, if everything is ok, the results seem to coincide with Matematica 4.1 with 10-digit precision.
This function is largely based at "Fortran library of special functions" which was converted to Matlab.Unfortunatey, the library can compute confluent hypergeometric function only for real values of a and b. So this file may be considered as its generalization for complex a and b.
This function also requires cgama.m file which computes Gamma function for complex variables. This file was taken from just the same "Fortran library" and insignificantly modified. |