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Topic: [HM] Binomial coefficients
Replies: 1   Last Post: Dec 3, 2002 4:52 AM

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David Fowler

Posts: 241
Registered: 12/3/04
Re: [HM] Binomial coefficients
Posted: Dec 3, 2002 4:52 AM
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Peter Flor <peter.flor@kfunigraz.ac.at> wrote:

<< Let C(m,n) be the binomial coefficient which is, I believe,
pronounced in English as "m choose n", i.e. C(m,0)=1,
C(m,n) = C(m,n-1)*(m-n+1)/n. If a is any complex number, not a
nonnegative integer, it is easy to derive the asymptotic
behaviour of the absolute value of C(a,n) as n goes to infinity.
I did not succeed in finding this formula in the literature,
except for a hint in "Analytic function theory" by Markushevich.
Could any group member kindly help me with a reference,
preferably a rather old one, since this is surely a classical
result? (The formula helps in deriving Abel's theorem on
convergence of the binomial series on the unit circle.) >>


Not what you are asking, but you might like to look at my article

The binomial coefficient function, American Mathematical Monthly, 103
(January 1996), 1-17. Also see the cover of the August-September
issue, 1995.

(The opening figures are very badly reproduced, but I can send a better
version to anyone who is interested.)

David Fowler






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