Games with integrate, infinity, symmetry, wxmaxima 0.7.1
Subject: Games with integrate, infinity, symmetry, wxmaxima 0.7.1
From: Milan Lukic
Date: Sat, 7 Jul 2007 21:13:59 -0700
* Richard Fateman <fateman at cs.berkeley.edu> [2007-07-07 11:07:31 -0700]:
> R:='integrate(sinh(x),x,-inf,inf)
> R,integrate; says principal value, 0. That's good.
>
> If you change the variable, eg. changevar(R,x=t+1,t,x) you get
> integrate(sinh(t+1),t,-inf-1,inf); I would hope to simplify -inf-1 to
> -inf, and there is a program, namely limit that does it. Limit(-inf-1) -->
> inf.
>
> However, limit ( the_integral...) doesn't do the job. That is, the -inf-1
> in the lower limit stays there.
>
> But the integral from -inf to inf of sinh(t+1) diverges. Maybe this is the
> right math answer?
I don't know about the -inf-1 => -inf issue, but I would like to say
that I think Maxima is correct on the divergence of
integrate(sinh(t+1),t,-inf,inf). Namely, the P.V. is defined as
limit(integrate(sinh(t+1),t,-R,R),R,+inf) which is
infinite. Graphically it is clear since the shift destroys the
symmetry you have in case integrate(sinh(x),x,-R,R).
HTH,
Milan
>
> For what it is worth, Mathematica 6.0 does not get R above, correct, even if
> you say to find Principal Value.
>
> RJF
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