A fast and accurate DE-formula algorithm to evaluate Ambartsumian-Chandrarasekhar $H$-function for isotropic scattering

In the present work, a compact, fast, and yet accurate algorithm is developed to calculate numerical values of Ambartsumian-Chandrasekhar’s \(H\)-function for isotropic scattering its moments on basis double exponential (DE) formula Takahashi Mori (RIMS, Kyoto Univ., 9:721, 1974). The main improvement made in new method an elimination iterative procedure automatic adjustment step-size integrations carried out with DE-formula. Instead, set optimal upper limit integration \(T_{\text{max}}\) number division points \(N_{\text{T}}\) specify quadrature predetermined calculations 15-digit accuracy, also another evaluations accuracy 14-digits or better. FORTRAN90 subroutines HFISCA HFMOMENT arbitrary degrees are subsequently constructed (their source codes driver together sample output shown Appendix this paper). Tables degree −1 through 6 by these programs presented. routines should prove useful not only astrophysical applications but other disciplines science such as electron transports condensed matter remote-sensing data analyses. A request copy Fortran 90 code program can be writing [email protected].