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From: mvm9745@acf4.UUCP (Michael V. Mascagni)
Newsgroups: net.math
Subject: Re: the derivative (actually the continuity) of x!
Message-ID: <920003@acf4.UUCP>
Date: Thu, 2-May-85 17:59:00 EDT
Article-I.D.: acf4.920003
Posted: Thu May  2 17:59:00 1985
Date-Received: Sat, 4-May-85 07:30:36 EDT
References: <318@muddcs.UUCP>
Organization: New York University
Lines: 11

It appears that the gamma function is unknown to this mathematician. To 
derive the gamma function from the usual multiplicative definition on
the integers, use the Euler product. It is not hard to show that the
gamma function is analytic on a real segment, and then by analytic
continuation to the complex plane with negative integral points deleted.
If one would like to stick to the integers, one can be made to look 
unnaturally restricted, since the complex field is determined by the ring of 
integers ... it is the algebraic closure of the completion of the field of
fractions of the ring of integers.           
                                         
                                           A.P. Mullhaupt