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: