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