Algorithm 912

Algorithm 912: a module for calculating cylindrical functions of complex order and complex argument. he present algorithm provides a module for calculating the cylindrical functions J ν (z), Y ν (z), H ν (1) (z), and H ν (2) (z), where the order ν is complex and the complex argument z satisfies -π<argz≤π. The algorithm is written in Fortran 90 and calculates the functions using real and complex numbers of any intrinsic data type whose kind type parameter the user’s Fortran system accepts. The methods of calculating the functions are based on two kinds of series expansions and numerical integration. Wronskian tests examine the functional values computed by this algorithm with double precision at 4,100,625 pseudorandom test points in the region | Re ν|≤60, | Im ν|≤60, | Re z|≤300, | Im z|≤300. From the results of the tests, we find that the errors of two kinds of Wronskians are less than 6·42×10 -14 .