Re: Few MMA questions - need some help!

*To*: mathgroup at christensen.cybernetics.net*Subject*: [mg1074] Re: Few MMA questions - need some help!*From*: rubin at msu.edu (Paul A. Rubin)*Date*: Fri, 12 May 1995 17:41:02 -0400*Organization*: Michigan State University

In article <3o6u1g$psn at news0.cybernetics.net>, pikus at dolphin.physics.ucsb.edu (Fedor G. Pikus) wrote: ->Hi, ->I need some help to make MMA do the calculation I want to: -> ->1. MMA 2.2 cannot take the following integral: -> Integrate[E^(s t) E^(I wmk t),{t,-Infinity,T}] ->even if I write -> Integrate[E^(s^2 t) E^(I wmk t),{t,-Infinity,T}] ->which defines that at -Infinity Exp goes to 0, it still cannot take it. ->MMA 2.0 did take this integral, and the one before, where it assumed ->positive s. This may be a bug in Integrate. I verified that kernel 2.2.2 cannot do it either; but if you combine the factors in the integrand, you get an answer: In[1]:= Integrate[ E^((s + I wkm) t), {t, -Infinity, T} ] Out[1]= T (s + I wkm) E -------------- s + I wkm ->The integral with finite limits -> Integrate[E^(s^2 t) E^(I wmk t),{t,-A,T}] ->can be computed, but the limit cannot. What it so difficult about ->limit of E^(s^2 t) at t-> -Infinity? Actually, I was about to say that I'm not sure the answer above is appropriate. You may be thinking that s is real, but Mathematica doesn't know that (and perhaps should not assume it). I assume you feel the limit is 0; but what if s = I? ->2. I need to make MMA compute the integrals like this: -> Int[t Sum[f[k],{k,Infinity}],{t,0,1}] ->and -> Int[If[m == n, t, t^2], {t,0,1}] ->to -> Sum[f[k],{k,Infinity}] ->and -> If[m == n, 1, 1/2] ->respectively. You can write your own integration function to do all this: In[1]:= Clear[ int ]; In[2]:= int[ x_ Sum[ z__ ], y_List ] := Sum[ z ] Integrate [x, y ] /; FreeQ[ z, y[[1]] ] In[3]:= int[ If[ a_, b_, c_ ], d_List ] := If[ a, Evaluate[ Integrate[ b, d ] ], Evaluate[ Integrate[ c, d ] ] ] In[4]:= int[ x_, y_List ] := Integrate[ x, y ] In[5]:= int[ t Sum[ f[k], {k, Infinity} ], {t, 0, 1} ] Out[5]= Sum[f[k], {k, Infinity}] ------------------------ 2 In[6]:= int[ If[ m== n, t, t^2 ], {t, 0, 1} ] Out[6]= 1 1 If[m == n, -, -] 2 3 Paul ************************************************************************** * Paul A. Rubin Phone: (517) 432-3509 * * Department of Management Fax: (517) 432-1111 * * Eli Broad Graduate School of Management Net: RUBIN at MSU.EDU * * Michigan State University * * East Lansing, MI 48824-1122 (USA) * ************************************************************************** Mathematicians are like Frenchmen: whenever you say something to them, they translate it into their own language, and at once it is something entirely different. J. W. v. GOETHE