Coulomb and Bessel functions of complex arguments and order
Journal of Computational Physics
Algorithm 714: CELEFUNT: a portable test package for complex elementary functions
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Mathematical Software (TOMS)
Algorithm 644: A portable package for Bessel functions of a complex argument and nonnegative order
ACM Transactions on Mathematical Software (TOMS)
Fortran 90/95 explained (2nd ed.)
Fortran 90/95 explained (2nd ed.)
Evaluation of the modified Bessel function of the third kind of imaginary orders
Journal of Computational Physics
The Mathematica Book
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Mathematical Software (TOMS)
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The present algorithm provides a module for calculating the cylindrical functions Jv(z), Yv(z), Hv(1)(z), and Hv(2)(z), where the order v is complex and the complex argument z satisfies −π z ≤ 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 v| ≤ 60, |Im v| ≤ 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.