Re: Re: delta function

*To*: mathgroup at smc.vnet.net*Subject*: [mg89950] Re: [mg89909] Re: delta function*From*: Daniel Lichtblau <danl at wolfram.com>*Date*: Wed, 25 Jun 2008 06:25:29 -0400 (EDT)*References*: <g3ihpo$fdt$1@smc.vnet.net> <200806240729.DAA10940@smc.vnet.net>

Magician wrote: > On Jun 21, 4:31 am, Magician <jadoo.d... at gmail.com> wrote: >> I am integrating over a function (not written in mathematica syntax) >> >> u=F(x) e^(- (x-xo)^2/t ) /t , >> i know in the limit t ->0, e^(- (x-xo)^2/t ) /t = delta(x-xo), but >> how do i get mathematica to recognize this. >> >> In mathematica, how can i construct hings like the Sokhotskyi-Plemelj >> formula ? > > hey somebody plz comment???? Here are a few comments. (1) Use Mathematica syntax to denote Mathematica expressions. (2) Use correct formulations. Your denominator is not correct, if what you seek is the effect of a delta function. (3) Don't throw in things that are irrelevant to your message. In this case, u=F(x) is irrelevant to your message. About that limit...yes, it might be useful to have it give a DiracDelta result. At present what one can do, in integrating a concrete function, is use Limit outside Integrate to get the effect of integration against a delta function. Example: ee = Exp[-(x-xo)^2/t]/t^(1/2); In[29]:= InputForm[Limit[Integrate[ee*x^2, {x,-Infinity,Infinity}], t->0, Assumptions->Element[{x,xo},Reals]]] Out[29]//InputForm= Sqrt[Pi]*xo^2 This has the advantage, moreover, of being mathematically correct whereas having Limit return a DiracDelta might go against some standard Limit behavior (I have not fully thought this out). Daniel Lichtblau Wolfram Research

**References**:**Re: delta function***From:*Magician <jadoo.dost@gmail.com>