Re: Problem with change of variables in an integral

*To*: mathgroup at smc.vnet.net*Subject*: [mg131571] Re: Problem with change of variables in an integral*From*: Murray Eisenberg <murrayeisenberg at gmail.com>*Date*: Thu, 5 Sep 2013 08:12:38 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-outx@smc.vnet.net*Delivered-to*: mathgroup-newsendx@smc.vnet.net*References*: <20130904033453.1EA336A15@smc.vnet.net>

First, I don't see how you can get the stated "correct result" unless your original function f[z] is specified -- presumably, to be 1/(1+z^3). Second, is Phi a fixed number 2 Pi/3 or is it a new variable (so that you're attempting to write the original single integral as a double integral)? At one place you seem to be setting Phi -> 2 Pi/3, yet in your "correct result" you show what seems to be a variable Phi. On Sep 3, 2013, at 11:34 PM, Dr. Robert Kragler <kragler at hs-weingarten.de> wrote: > > Hello, > > Although I know how to make a change of variables in an integral I can only do > it manually by applying a substitution rule to the integrand and the > differential e.g > {f[z],\[DifferentialD]z}//. {z-> r E^(I > \[Phi]),\[DifferentialD]z->E^(I \[Phi]) \[DifferentialD]r,\[Phi] -> (2\[Pi])/3} > > But it cannot applied this substitution rule directly to the integral, e.g. > Integrate[f[z],{z,0,\[Infinity]}] //. {z-> r E^(I > \[Phi]),\[DifferentialD]z->E^(I \[Phi]) \[DifferentialD]r,\[Phi] -> (2\[Pi])/3} > > Comparing with the correct result, the exponential factor E^((2 I \[Pi])/3) = > (-1)^(2/3) is missing in the evaluation of the integral. The correct appearance > of the > integral is : Integrate[1/(1+r^3) E^((2 I \[Pi])/3),{r,0,\[Infinity]}] > > How can I force Mathematica (V8) to perform the correct transformation of > variables as regards to the integral (and not to its separate parts of it as > {f[z],\[DifferentialD]z} ? > > Any suggestions are appreciated. > Robert Kragler > > -- > Robert Kragler > Email : kragler at hs-weingarten.de > URL : http://portal.hs-weingarten.de/web/kragler --- Murray Eisenberg murray at math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower University of Massachusetts 710 North Pleasant Street Amherst, MA 01003-9305

**References**:**Problem with change of variables in an integral***From:*"Dr. Robert Kragler" <kragler@hs-weingarten.de>