kvanston@muddcs.UUCP (Kathryn Vanstone) (05/10/85)
*** REPLACE THIS LINE WITH YOUR REBUTTAL *** >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. Of course I know about the Gamma function! (i'd better...I've just taken a test in Bessel functions). So did the people in net.puzzle. The Gamma function is differentiable everywhere (on the reals) except the non-positive integers. However, several people in net.puzzle claimed that x! was not continuous when defined on the integers, and I wanted to point out that that statement is false. The discussion on the derivative of the Gamma function did not need comment. So I wasn't so much commenting on the answer (except to state that I would request a definition of the space that x! was defined over), but on the discussion of the answer. I probably should have included a copy of some of the discussions, but I haven't got the hang of this net yet. Kathryn Van Stone Harvey Mudd College <Oh, well, I don't remember this part...> "Led go by dose, your hurdig be!"