11/18/2009, 10:43 AM

(11/18/2009, 09:55 AM)mike3 Wrote: I looked at it and I'm not sure what to make of what's there. The locations of the singularities seem to be involved in the proof, but given the "universality" of the coefficients mentioned, it appears they may not be needed for their construction (as different functions have different singularities).

Yes, there you are right (and i was wrong). If I remember correctly you only need the Runge approximation for 1/(z-w) or so. So if you have the coefficients of the Runge approximation maybe you can deduce the Star-expansion coefficients following the proof.

But I really wonder why the coefficients are not given in the Springer online reference. I was inclined to think that they are quite complicated.

Quote:Though I wonder then why it was referenced on the website

Indeed I wonder too. It mentions Painlevé having explicitely found the coefficients, but the given references are not by Painlevé, not even mentioned in [2]. I think it is just an oversight, forgetting/or being to lazy to give the proper references.

In wikipedia the Mittag-Leffler expansion is also mentioned but with rather soft text-book references, which surely dont contain the coefficient computations.