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Re: Symbolic integration

• To: mathgroup at smc.vnet.net
• Subject: [mg102630] Re: [mg102592] Symbolic integration
• From: "Elton Kurt TeKolste" <tekolste at fastmail.us>
• Date: Mon, 17 Aug 2009 04:04:42 -0400 (EDT)
• References: <200908161039.GAA01165@smc.vnet.net>

(* This will read a lot easier if you copy it (one line at a time) back
into Mathematica *)

First : fix the use of square brackets: they should be parentheses.

In[14]:= \[Lambda] -> (2^(-2/\[Nu])
(Gamma[1/\[Nu]]/Gamma[3/\[Nu]]))^(-1/2)

Out[14]= \[Lambda] -> 1/Sqrt[(2^(-2/\[Nu])
Gamma[1/\[Nu]])/Gamma[3/\[Nu]]]

Second, you have created a rule, which does not assign a value to
\[Lambda] .  Simply replace the -> with  =.

In[18]:= \[Lambda] = (2^(-2/\[Nu])
(Gamma[1/\[Nu]]/Gamma[3/\[Nu]]))^(-1/2)

Out[18]= 1/Sqrt[(2^(-2/\[Nu]) Gamma[1/\[Nu]])/Gamma[3/\[Nu]]]

Now the desired value for \[Lambda] appears in the integral, but
Mathematica does not automatically simplify it.

Integrate[\[Nu] E[-0.5 Abs[
       z/\[Lambda]]^\[Nu]]/(\[Lambda] 2^(1 + 1/\[Nu]) Gamma[1/\[Nu]]),
       z]

Out[19]= (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]]

In[21]:= Simplify[%18]

Out[21]= 1/Sqrt[(4^(-1/\[Nu]) Gamma[1/\[Nu]])/Gamma[3/\[Nu]]]

On Sun, 16 Aug 2009 06:39 -0400, "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
> 
Regards,
Kurt Tekolste

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