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Re: Symbolic integration

  • To: mathgroup at smc.vnet.net
  • Subject: [mg102658] Re: [mg102592] Symbolic integration
  • From: tzygmund mcfarlane <tzygmund at googlemail.com>
  • Date: Mon, 17 Aug 2009 08:07:18 -0400 (EDT)
  • References: <200908161039.GAA01165@smc.vnet.net>

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<btreat1 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 <tzygmund 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
>>
>
>
>
> --
> DrMajorBob at bigfoot.com
>


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