ForAll testing equality, and Limit evaluating wrong

*To*: mathgroup at smc.vnet.net*Subject*: [mg104512] ForAll testing equality, and Limit evaluating wrong*From*: Rui <rui.rojo at gmail.com>*Date*: Tue, 3 Nov 2009 02:50:55 -0500 (EST)

I want to prove that xTransf2[f]==xTransf[f] for all f multiple of 1/24. xTransf2[f_]:=36 Sinc[6 Pi f]^2 and xTransf[f]:=Limit[(E^(-24 I r \[Pi]) (-Cos[12 r \[Pi]] + Cos[24 r \ [Pi]] + 12 r \[Pi] Sin[24 r \[Pi]]))/(2 r^2 \[Pi]^2), r->f] If I do ForAll[f \[Element] Integers, YTransf[f/24] == YTransf2[f/24]] I don't get a result... I can't find a way. In fact, I get (144 E^(-I f \[Pi]) (-2 Cos[(f \[Pi])/2] + 2 Cos[f \[Pi]] + f \[Pi] Sin[f \[Pi]]))/(f^2 \[Pi]^2) == 36 Sinc[(f \[Pi])/4]^2 They are clrealy equal, at least on the 48 points closest to 0, because if I do And @@ ((xTransf[1/24 #] == xTransf2[1/24 #]) & /@ Range[-24, 24]) I get "True" Any pretty way to be certain? I've also realised that Mathematica has evaluated Limits with variables, making the "Limit" disappear when for some values of the variables I could get an indetermined result with the evaluated version. For example, the Limit in xTransf xTransf[f] I get (E^(-24 I f \[Pi]) (-Cos[12 f \[Pi]] + Cos[24 f \[Pi]] + 12 f \[Pi] Sin[24 f \[Pi]]))/(2 f^2 \[Pi]^2) without the Limit. So, if I do xTransf[f]/.f->0 I get errors but if I do xTransf[0] I get 36 ... Hope you can help :)

**Follow-Ups**:**Re: ForAll testing equality, and Limit evaluating wrong***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>

**Re: ForAll testing equality, and Limit evaluating wrong***From:*Rui Rojo <rui.rojo@gmail.com>

**Re: ForAll testing equality, and Limit evaluating wrong***From:*DrMajorBob <btreat1@austin.rr.com>

**Re: ForAll testing equality, and Limit evaluating wrong***From:*Rui Rojo <rui.rojo@gmail.com>

**Re: ForAll testing equality, and Limit evaluating wrong***From:*DrMajorBob <btreat1@austin.rr.com>

**Re: ForAll testing equality, and Limit evaluating wrong***From:*Rui Rojo <rui.rojo@gmail.com>

**Re: ForAll testing equality, and Limit evaluating wrong***From:*DrMajorBob <btreat1@austin.rr.com>