expintegral_e: series failed



On 01/03/2012 02:48 PM, Raymond Toy wrote:
> On Tue, Jan 3, 2012 at 1:25 PM, dlakelan <dlakelan at street-artists.org>wrote:
> 
>> On 12/30/2011 12:13 AM, Raymond Toy wrote:
>>> Could you file a bug report on this?  I know about some of these issues
>> and
>>> am working on them (slowly).  The basic parts work, but the corner cases
>>> need more work (especically since my approach fails in some cases where
>> the
>>> original gave correct answers).
>>
>> 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
>>
>>
> Thanks for the tip.  I had not seen this; I was working from the continued
> fraction and series representations of the incomplete gamma function.
> 
> This seems interesting, but it's not immediately clear if "all a and x"
> means all real a and x or all complex a and x.

Agreed, and the article seems to treat all the parameters as real,
though perhaps the author has worked out whether the method makes sense
for complex parameters or requires some modification?

In any case, perhaps the real case is the most common, and it could be
useful to use this result for evaluation when the parameters are real.