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Re: [HM] Binomial coefficients
Posted:
Dec 3, 2002 4:52 AM


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,n1)*(mn+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), 117. Also see the cover of the AugustSeptember issue, 1995.
(The opening figures are very badly reproduced, but I can send a better version to anyone who is interested.)
David Fowler



