expintegral_e: series failed



On 4/01/2012 8:25 AM, dlakelan wrote:
>
> I'm sure you've seen this since the simplest google search would bring
> it up, but it seemed interesting so if you haven't seen it you might
> want to take a look:
>
> http://iopscience.iop.org/0295-5075/71/1/001/pdf/epl_71_1_001.pdf
This reference is also freely available as 
http://arxiv.org/abs/math-ph/0501019

Asymptotic and exact series representations for the incomplete Gamma 
function
Authors: Paolo Amore

Abstract: Using a variational approach, two new series representations 
for the incomplete Gamma function are derived: the first is an 
asymptotic series, which contains and improves over the standard 
asymptotic expansion; the second is a uniformly convergent series, 
completely analytical, which can be used to obtain arbitrarily accurate 
estimates of $\Gamma(a,x)$ for any value of $a$ or $x$. Applications of 
these formulas are discussed.

Journal reference: Europhysics Letters 71, 1-7 (2005)