Talk:Confluent hypergeometric function

Whattaker function

Is U(a,b,z) the Whittaker function? (anon, Oct 2006)

I don't know, that's not what A&S calls them.linas 00:43, 11 December 2006 (UTC)

I am certainly not an expert, but I now know a bit about Kummer/Whittaker functions. Enough to find severe discrepancies between A&S and maple. Anybody have an opinion about whether I should tack some things up on the main page?

Kummer's function

I am interested in the real part of Kummmer's function in the case a=2n+1, b=a+1 (real part of incomplete gamma). From a numerical point of view, which is cheaper to approximate, what is the convergence like for each and what methods are used? (anon, Nov 2006)

continuous fraction for e^z

The original text used to say

by setting b = 0 and c = 1

It is hard to tell what it meant because there was no c around.

M(1, 2, z)⁄M(0, 1, z)
= 1/
1 − 1⁄2 z/
1 + 1⁄6 z/
1 − 2⁄12 z/
1 + 2⁄20 z/
…
1 − k⁄(2 k − 1) (2 k) z/
1 + k⁄(2 k) (2 k + 1) z/
…
= 1 + 1/ 1 − 1⁄2 z/
1 + 1⁄6 z/
1 − 1⁄6 z/
1 + 1⁄10 z/
…
1 − 1⁄2 (2 k − 1) z/
1 + 1⁄2 (2 k + 1) z/
…

Transforming this fraction with the sequence (1, 2, 3, 2, …, 2 k + 1, 2, …) gives

1/
1 − z/
2 + z/
3 − z/
2 + z/
…
(2 k − 1) − z/
2 + z/
…
= (e^z − 1)⁄z

which is not quite what was postulated.

--Yecril (talk) 13:47, 3 October 2008 (UTC)

Formal power series?

The following is simply too cryptic for inclusion as it stands

Moreover,

$U(a,b,z)=z^{-a}\cdot \,_{2}F_{0}\left(a,1+a-b;\,;-{\frac {1}{z}}\right),$

where the hypergeometric series $_{2}F_{0}(\cdot ,\cdot ;;z)$ degenerates to a formal power series in z (which converges nowhere).

Please explain precisely what it is that this is supposed to convey, including a reference. Sławomir Biały (talk) 18:37, 3 July 2009 (UTC)