Algorithm 822: GIZ, HIZ: two Fortran 77 routines for the computation of complex Scorer functions

Two Fortran 77 routines for the evaluation of Scorer functions of complex arguments Gi(z), Hi(z), and their derivatives are presented. The routines are based on the use of quadrature, Maclaurin series, and asymptotic expansions. For real z, comparison with a previous code by A. J. MacLeod [1994] is provided.

[1]  D. E. Amos.  Algorithm 644: A portable package for Bessel functions of a complex argument and nonnegative order , 1986, TOMS.

[2]  Soo-Y. Lee,et al.  The inhomogeneous Airy functions, Gi(z) and Hi(z) , 1980 .

[3]  Bertha Jeffreys,et al.  The use of the Airy functions in a potential barrier problem , 1956, Mathematical Proceedings of the Cambridge Philosophical Society.

[4]  Allan J. MacLeod,et al.  Computation of inhomogeneous Airy functions , 1994 .

[5]  F. Olver.  Asymptotics and Special Functions , 1974 .

[6]  Nico M. Temme,et al.  On the zeros of the Scorer functions , 2003, J. Approx. Theory.

[7]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[8]  K. S. Kölbig,et al.  Errata: Milton Abramowitz and Irene A. Stegun, editors, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, Applied Mathematics Series, No. 55, U.S. Government Printing Office, Washington, D.C., 1994, and all known reprints , 1972 .

[9]  Nico M. Temme,et al.  On nonoscillating integrals for computing inhomogeneous Airy functions , 2001, Math. Comput..

[10]  Nico M. Temme,et al.  Algorithm 819: AIZ, BIZ: two Fortran 77 routines for the computation of complex Airy functions , 2002, TOMS.

[11]  W. Happer,et al.  Inhomogeneously broadened spin masers , 1999 .

[12]  Nico M. Temme,et al.  Computing Complex Airy Functions by Numerical Quadrature , 2002, Numerical Algorithms.

[13]  William J. Cody,et al.  The use of Taylor series to test accuracy of function programs , 1991, TOMS.