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Re: Symbolic integration

• To: mathgroup at smc.vnet.net
• Subject: [mg102685] Re: Symbolic integration
• From: tzygmund <tzygmund at googlemail.com>
• Date: Tue, 18 Aug 2009 06:11:12 -0400 (EDT)
• References: <200908161039.GAA01165@smc.vnet.net> <h6bh5c$6pi$1@smc.vnet.net>

Thanks to all of you who replied, with the level of sophistication I
would expect on the Mathematica board.

Leonid, why would I not want to have an absolute value function inside
the exponent?

Thanks

On Aug 17, 1:07 pm, tzygmund mcfarlane <tzygm... at googlemail.com>
wrote:
> I should have known better than to write to the mailing list within my
> first hour of starting to use a new software. I went and RTM. Here is
> what I intended:
>
> ******************************
> \[Lambda] = (2^(-2/\[Nu]) Gamma[1/\[Nu]]/Gamma[3/\[Nu]])^(-1/2);
>
> Integrate[(\[Nu] *
>    Exp[-0.5 *Abs[z/ \[Lambda]]^\[Nu]]/(\[Lambda]* 2^(1 + 1/\[Nu])*
>     Gamma[1/\[Nu]])), {z, -\[Infinity], +\[Infinity]}]
> ******************************
>
> Thanks for your comment.
>
>
>
> On Mon, Aug 17, 2009 at 4:54 AM, DrMajorBob<btre... at austin.rr.com> wrote:
> > The integral can't be computed:
>
> > Integrate[\[Nu] E[-0.5   Abs[
> >       z/ \[Lambda]]^\[Nu]]/(\[Lambda] 2^(1 + 1/\[Nu]) Gamma[
> >      1/\[Nu]]), z]
>
> > (2^(-1 - 1/\[Nu]) \[Nu] \[Integral]E[-0.5 Abs[
> >      z/\[Lambda]]^\[Nu]] \[DifferentialD]z)/(\[Lambda] Gamma[1/\[=
Nu=
> ]]
> >  )
>
> > Maybe you meant the first line to be
>
> > \[Lambda] = (2^(-2/\[Nu]) Gamma[1/\[Nu]]/  Gamma[3/\[Nu]])^(-1/2);
>
> > (parentheses for power, not brackets) and then the integral is still
> > undefined:
>
> > Integrate[\[Nu] E[-0.5   Abs[
> >       z/ \[Lambda]]^\[Nu]]/(\[Lambda] 2^(1 + 1/\[Nu]) Gamma[
> >      1/\[Nu]]), z]
>
> > (2^(-1 - 1/\[Nu]) \[Nu] Sqrt[(2^(-2/\[Nu]) Gamma[1/\[Nu]])/
> >  Gamma[3/\[Nu]]] \[Integral]E[-0.5 2^(-\[Nu] Re[1/\[Nu]])
> >      Abs[z]^\[Nu] Abs[Gamma[1/\[Nu]]/Gamma[3/\[Nu]]]^(\[Nu]/
> >      2)] \[DifferentialD]z)/Gamma[1/\[Nu]]
>
> > But I doubt that's what you intended, either.
>
> > Bobby
>
> > On Sun, 16 Aug 2009 05:39:45 -0500, tzygmund <tzygm... at googlemail.com>
> > wrote:
>
> >> Hi,
>
> >> I have a fairly simple question which I cannot solve. I want to assign
> >> a symbolic expression to a greek letter and then use this in a
> >> subsequent integral. So,
> >> ********************************
> >> \[Lambda] -> [
> >> \!\(\*SuperscriptBox["2",
> >> RowBox[{"[",
> >> FractionBox[
> >> RowBox[{"-", "2"}], "\[Nu]"], "]"}]]\) Gamma[1/\[Nu]]/
> >>   Gamma[3/\[Nu]]]^(-1/2)
>
> >> Integrate[\[Nu] E[-0.5   Abs[z/ \[Lambda]]^\[Nu]]/(\[Lambda] 2^(1 +
> >>     1/\[Nu]) Gamma[1/\[Nu]]), z]
> >> **********************************
>
> >> How can I get this to work?
>
> >> Thanks
>
> > --
> > DrMajor... at bigfoot.com

• References:
  • Symbolic integration
    • From: tzygmund <tzygmund@googlemail.com>