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Mittag-Leffler series for generating continuum sum?
#14
(11/18/2009, 08:05 AM)bo198214 Wrote: Mike, you didnt read what I wrote (again!, why do I give all the extra information?), I clearly said that I found the djvu on the web.
And if you are really interested then you type "A.I. Markushevich, Theory of functions of a complex variable, djvu" in the google field and get it too and can read the 1965 edition yourself. In its construction it mentions the Runge polynomial approximation, perhaps there you can find the coefficients.

See, for me it takes off 2 hours from my sparse time to go to a library. And this for a book I am not even sure whether it contains the needed information.

Ah. I guess I just missed the bit where you said "internet".

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).

It still doesn't seem to give anything useful for the construction. I also found a limited book preview for the 1977 edition on Google, the second page of the proof is omitted and it seems the section ends right after that page. Given the length of the proof (2 pages) in the 1965 book, I'm also not sure if this 1977 book would contain the method either, so yeah, I could understand your concern about taking the time to go to the library! Smile Though I wonder then why it was referenced on the website, but perhaps maybe that's just because the book may, like the 1965 edition, just mention the fact they are universal, not actually construct them, and the actual construction may be in the French-language paper by Borel, or something it references.
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RE: Mittag-Leffler series for generating continuum sum? - by mike3 - 11/18/2009, 09:55 AM

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