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>
- Symbolic integration