ZHYPG2 Library "JINRLIB" Author: O.Chuluunbaatar You are Language: Fortran visitor here. Calculation of the hypergeometric functions with complex parameters and complex argument The function ZHYPG2 computes the hypergeometric functions with complex parameters , and an argument [1]. For calculation of the hypergeometric function it used the beforehand calculated values of the hypergeometric functions and their derivatives by means of the subroutine HYPGEO [2] at points The considered procedure was constructed on the basis of the algorithms published in [3]. The described algorithm allows one to save calculation time of the multidimensional integrals, whose kernel contains hypergeometric functions , approximately 10-60 times depending on accuracy of the calculation (10^{-4}-10^{-14}) in comparison with a direct use of the subroutine HYPGEO at each value . This type of calculations occurs in investigation of the single and double ionizations by electron impact of two-nuclear molecules (see papers [4,5]). References: ----------- 1. Abramowitz M. and Stegun I. Handbook of mathematical functions, National Bureau of Standards Applied Mathematics series. 55. 1964. 2. Press W.H., Teukolsky S.A., Vetterling W.T. and Flannery B.P. Numerical recipes: The art of scientific computing. Cambridge University Press, Cambridge, 1986. 3. Chuluunbaatar O. Bulletin of Tver State University: Ser. Applied Mathematics. 2008, N = 26(86), pp. 47-64. 4. Chuluunbaatar O., Joulakian B.B., Tsookhuu Kh. and Vinitsky S.I. J. Phys. B, 2004, v. 37, pp. 2607-2616. 5. Chuluunbaatar O., Joulakian B.B., Puzynin I.V., Tsookhuu Kh. and Vinitsky S.I. J. Phys. B, 2008, v. 41, pp.015204-1-6. Structure: ---------- FUNCTION Name: ZHYPG2 Internal subroutines: ZSUM, ZGAMMA, DRHYP, CGAMA, HYPGEO, HYPDRV, HYPSER, ODEINT, BSSTEP, MMID, PZEXTR Usage: ------ ZFUNC = ZHYPG2(ZA,ZC,ZZ,NMAX,EPS) INPUT: ZA, ZC, ZZ, NMAX, EPS: ZA - double complex number, contains value of parameter ZC - double complex number, contains value of parameter . ZZ - double complex number, contains value of argument . NMAX - integer number, the maximum number of summation of truncated Gaussian series. EPS - double precision number, given accuracy. Sources with example and description are submitted. Example: |