[Help-gsl] Bug in implementing Kummer's U?

[George Japaridze]

Hi,

There is strange problem with the Kummer's confluent hypergeometric  
function U.

The relation I am using between U and confluent hypergeometric 1F1 is  
from Abramowitz, Stegun, relation 13.1.3, in there I choose b=0.5 (as  
I understand, U is implemented a'la Abramowitz, Stegun)

U(a, 0.5 ,z) = sqrt(pi) ( 1F1(a, 0.5, z)/gamma(a+0.5) - 2*sqrt(z)*1F1 
(a+0.5, 1.5, z)/gamma(a) )		(1)

Now, when I calculate in GSL function U (left hand side of (1)), or  
the right hand side of (1), I get the following result (in this  
example a = 0.2):

1) Left and right hand sides approximately yield the same values for  
z less 30, e.g. for
z=10 - LHS=RHS=0.622885 (my old version with Mathematica with only  
1F1 implemented confirms that for the RHS value).

z=20 - RHS = LHS = 0.545614

2) left and right hand sides DRASTICALLY differ for large z, e.g.
z=40 - LHS = 0.476, RHS = -482
z=60 - LHS = 0.44, RHS = 6.1 10^(10)

and the difference grows with z increasing.

The macros for a LHS and RHS are attached.

Any ideas? how the special functions for a large values of arguments  
are tabulated in GSL? Can it be bug in implementing U?
It's kinda pressing issue for me, so I would appreciate any help or  
bug shook out from my macros..

Thanks,

George Japaridze

Kummer_LHS.c
Description: Binary data

Kummer_RHS.c
Description: Binary data