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

**From**: |
George Japaridze |

**Subject**: |
[Help-gsl] Bug in implementing Kummer's U? |

**Date**: |
Sun, 5 Feb 2006 19:50:18 -0500 |

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

**[Help-gsl] Bug in implementing Kummer's U?**,
*George Japaridze* **<=**