What are the magic constants in this formula?
mike3
I read this website:
http://eom.springer.de/s/s087230.htm
It mentions a "Mittag-Leffler expansion" for an analytic complex
function across its Mittag-Leffler star using an infinite sum of
polynomials which involves the Taylor coefficients as well as some
other magic coefficients and term counts that are said to be
independent of the specific function, and that these can be "evaluated
once and for all". But what is the process, algorithm, or formula by
which one can evaluate these magic numbers? I can't get at the
references as I don't have ready access to an academic library (too
much distance), and even if I did one of them is in French, a language
I do not know.
mike3
> Hi.
>
> I read this website:
>
> http://eom.springer.de/s/s087230.htm
>
> function across itsMittag-Lefflerstar using an infinite sum of
> polynomials which involves the Taylor coefficients as well as some
> other magic coefficients and term counts that are said to be
> independent of the specific function, and that these can be "evaluated
> once and for all". But what is the process, algorithm, or formula by
> which one can evaluate these magic numbers? I can't get at the
> references as I don't have ready access to an academic library (too
> much distance), and even if I did one of them is in French, a language
> I do not know.
Any answer?
mike3
This one is really tough because I haven't been able to get a hand on
any
references that are useful. I found Borel's book online but as I said,
it's in French, so I could not make a lot of use of it. Is there an
English
translation? I'm really frustrated, and am wondering why I receive no
response here. Is it that obscure?
master1729
they simply dont know.
in sci.math there are 3 ways :
1) they know the answer and respond that you are talking about ' trivial things everybody already knows ' with or without insults or further belittling.
2) they dont know and wont admit they dont know it to save their face. they will avoid posting like hell.
3) they misunderstand , insult or give a wrong answer , usually ending up in a flame war or in 1) or 2). Often using terms like ' useless ' and ' crank ' and in case of a nonstandard idea ' idiot '. Poe's law might sneak into the followup posts.
i asked similar questions to yours mike3 and got no decent replies either.
im not really amazed this happens again.
circular reasoning is also very common.
( example : 3-body problem -> 'diff eq' -> no closed form remarked -> sundman mentioned -> sundman did not solve it remarked -> what are you talking about , we have 'diff eq' ( ending back in step 2 after 150 posts ) )
( example 2 : any thread about set theory with more than 100 posts )
regards
tommy1729
mike3
<SNIP>
But the thing here is, I'm not asking for something "nonstandard" or
trying to
propose some kind of "crank" theory, rather I'm asking for the details
of a
known result found by non-"crank", "real" mathematicians.
FredJeffries
Chapter 11 of Hille's Analytic Function Theory, "Singularities and
Representation of Analytic Functions" is partially available through
Google Books:
Start on page 38. You (or someone more knowledgeable than I) may be
able to dig something out, but it seems that the section of interest
to you, 11.4 "Analytic Continuation in a Star" is missing from the
preview.
Also, Volume 3 of Markushevich's Theory of Functions of a Complex
Variable, chapter 8, section 41 "Analytic Continuation in a Star" is
also partially available.
Search for the phrase "Mittag-Leffler Star". Alas, the second half of
the proof is not included in the preview!
mike3
> On Nov 18, 1:03 am, mike3 <mike4...@yahoo.com> wrote:
>
>
>
> > Hi.
>
> > I read this website:
>
> >http://eom.springer.de/s/s087230.htm
>
> > It mentions a "Mittag-Leffler expansion" for an analytic complex
> > function across its Mittag-Leffler star using an infinite sum of
> > polynomials which involves the Taylor coefficients as well as some
> > other magic coefficients and term counts that are said to be
> > independent of the specific function, and that these can be "evaluated
> > once and for all". But what is the process, algorithm, or formula by
> > which one can evaluate these magic numbers? I can't get at the
> > references as I don't have ready access to an academic library (too
> > much distance), and even if I did one of them is in French, a language
> > I do not know.
>
> Chapter 11 of Hille's Analytic Function Theory, "Singularities and
> Representation of Analytic Functions" is partially available through
> Google Books:
>
>
> Start on page 38. You (or someone more knowledgeable than I) may be
> able to dig something out, but it seems that the section of interest
> to you, 11.4 "Analytic Continuation in a Star" is missing from the
> preview.
>
> Also, Volume 3 of Markushevich's Theory of Functions of a Complex
> Variable, chapter 8, section 41 "Analytic Continuation in a Star" is
> also partially available.
>
>
> Search for the phrase "Mittag-Leffler Star". Alas, the second half of
> the proof is not included in the preview!
Yes, I know, it's aggravating, and this is the type of stone wall I've
been running against... not having access to a good academic library
really sucks.
master1729
i know.
but that is irrelevant. (as you can see yourself)
regards
tommy1729