hyper1f1.h

用matlab语言编写的试井分析的程序

/*************************************************************************
Cephes Math Library Release 2.8:  June, 2000
Copyright by Stephen L. Moshier

Contributors:
    * Sergey Bochkanov (ALGLIB project). Translation from C to
      pseudocode.

See subroutines comments for additional copyrights.

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*************************************************************************/

#ifndef _hyper1f1_h
#define _hyper1f1_h

#include "ap.h"

#include "gammaf.h"


/*************************************************************************
Confluent hypergeometric function

Computes the confluent hypergeometric function

                         1           2
                      a x    a(a+1) x
  F ( a,b;x )  =  1 + ---- + --------- + ...
 1 1                  b 1!   b(b+1) 2!

Many higher transcendental functions are special cases of
this power series.

As is evident from the formula, b must not be a negative
integer or zero unless a is an integer with 0 >= a > b.

The routine attempts both a direct summation of the series
and an asymptotic expansion.  In each case error due to
roundoff, cancellation, and nonconvergence is estimated.
The result with smaller estimated error is returned.



ACCURACY:

Tested at random points (a, b, x), all three variables
ranging from 0 to 30.
                     Relative error:
arithmetic   domain     # trials      peak         rms
   DEC       0,30         2000       1.2e-15     1.3e-16
 qtst1:
 21800   max =  1.4200E-14   rms =  1.0841E-15  ave = -5.3640E-17
 ltstd:
 25500   max = 1.2759e-14   rms = 3.7155e-16  ave = 1.5384e-18
   IEEE      0,30        30000       1.8e-14     1.1e-15

Larger errors can be observed when b is near a negative
integer or zero.  Certain combinations of arguments yield
serious cancellation error in the power series summation
and also are not in the region of near convergence of the
asymptotic series.  An error message is printed if the
self-estimated relative error is greater than 1.0e-12.

Cephes Math Library Release 2.8:  June, 2000
Copyright 1984, 1987, 1988, 2000 by Stephen L. Moshier
*************************************************************************/
double hypergeometric1f1(double a, double b, double x);


#endif