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From: quiroz@rochester.UUCP (Cesar Quiroz)
Newsgroups: net.math
Subject: Re: infinite differentiation
Message-ID: <4155@rochester.UUCP>
Date: Mon, 12-Dec-83 21:48:34 EST
Article-I.D.: rocheste.4155
Posted: Mon Dec 12 21:48:34 1983
Date-Received: Tue, 13-Dec-83 06:41:57 EST
References: <2087@allegra.UUCP>
Organization: U. of Rochester, CS Dept.
Lines: 19


      In a word :

		exp(D) = 1 + D + ... + (D^n)/n! + ... (as operators)

		so:

		exp(D) f(x) = f(x) + Df(x) + D^2 f(x) /2! + ...D^n f(x) / n! ...

			    = sum [ D^i f(x) / i! * ((x+1) -x)^i ] i= 0,1,...

			    = Taylor expansion for f around x, eval. at 1

			    = f(x+1)


							Cesar Quiroz
							UofR Comp Sc Dpt.