The asymptotics of factorials, binomial coefficients and Catalan numbers

David Kessler and Jeremy Schiff

We present a variety of novel asymptotic series for factorials, binomial coefficients and Catalan numbers, all having only even or odd powers.

Publication information: We submitted this to the American Mathematical Monthly, but it was rejected (if you are interested you can click here for the referee reports and read the editor's comments below). We are trying to work out where to send it next.


From Thu May 11 21:45:33 2006
Date: Thu, 11 May 2006 13:44:40 -0400
From: American Mathematical Monthly <>
Cc: American Mathematical Monthly <>
Subject: Submission to the Monthly #06-0226

Dear Professor Schiff,

I am writing about your paper "The Asymptotics of Factorials,
Binomial Coefficients and Catalan Numbers" (manuscript #06-0226),
which you submitted to the American Mathematical Monthly.  Attached
please find the referees' reports.

Although both referees have positive things to say about this paper,
one of them thinks that it doesn't belong in the Monthly.  Even the
referee who recommends publication notes that the paper is fairly
specialized and technical, and says that it will only grab the
interest of a limited number of readers.  Based on these reservations
from the referees, my conclusion is that the Monthly is not the right
journal for this paper, and I cannot accept it for publication.  I
hope you'll be able to publish it in another journal--it deserves to
be published.

Although we are unable to accept your paper for publication, please
accept our thanks for thinking of the Monthly.


Daniel J. Velleman