What's wrong with this integral in mathematica?
- To: mathgroup at smc.vnet.net
- Subject: [mg60673] What's wrong with this integral in mathematica?
- From: "kiki" <lunaliu3 at yahoo.com>
- Date: Fri, 23 Sep 2005 04:20:49 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Hi all, I am evaluating this integral: \!\(Integrate[\(\[ExponentialE]\^\(\[ImaginaryI]\ a\ z\)\ Sinh[z]\)\/\((b + \ Cosh[z])\)\^2, {z, \(-?\), ?}, Assumptions \[Rule] \ {a > 0, b > 1}]\) After 1 hour running, it generates the following huge result: (after simplification) But even using my pencil and paper, do it manually, I should get much simpler result... Can anybody tell me what's wrong? --------------------------------------------------- \!\(\((\(( 1 + b - \@\(\(-1\) + b\^2\))\)\^\(\(-\[ImaginaryI]\)\ a\)\ \((1 + b + \ \@\(\(-1\) + b\^2\))\)\^\(\(-\[ImaginaryI]\)\ a\)\ \((4\ a\ \((4 + 4\ \ \[ImaginaryI]\ a + a\^2 + \[ImaginaryI]\ a\^3)\)\ \@\(\(-1\) + b\^2\)\ \((1 + \ b - \@\(\(-1\) + b\^2\))\)\^\(\[ImaginaryI]\ a\)\ \((1 + b + \@\(\(-1\) + b\^2\))\)\^\(\[ImaginaryI]\ a\)\ AppellF1[1 - \[ImaginaryI]\ a, 2, 2, 2 - \[ImaginaryI]\ a, \ \(-\(1\/\(b + \@\(\(-1\) + b\^2\)\)\)\), 1\/\(\(-b\) + \@\(\(-1\) + b\^2\)\)] \ + \((\[ImaginaryI] + a)\)\ \((4\ a\ \((\(-2\)\ \[ImaginaryI] + 3\ a + \ \[ImaginaryI]\ a\^2)\)\ b\ \@\(\(-1\) + b\^2\)\ \((1 + b - \@\(\(-1\) + \ b\^2\))\)\^\(\[ImaginaryI]\ a\)\ \((1 + b + \@\(\(-1\) + b\^2\))\)\^\(\ \[ImaginaryI]\ a\)\ AppellF1[2 - \[ImaginaryI]\ a, 2, 2, 3 - \[ImaginaryI]\ a, \(-\(1\/\(b + \@\(\(-1\) + b\^2\)\)\)\), 1\/\(\(- b\) + \@\(\(-1\) + b\^2\)\)] + \((2\ \[ImaginaryI] + a)\)\ \((4\ \((2 + \[ImaginaryI]\ a)\)\ a\ \@\(\(-1\) + \ b\^2\)\ \((1 + b - \@\(\(-1\) + b\^2\))\)\^\(\[ImaginaryI]\ a\)\ \((1 + b + \ \@\(\(-1\) + b\^2\))\)\^\(\[ImaginaryI]\ a\)\ AppellF1[1 \ + \[ImaginaryI]\ a, 2, 2, 2 + \[ImaginaryI]\ a, \(-\(1\/\(b + \@\(\(-1\) + b\^2\)\)\)\), 1\/\(\(-b\) + \@\(\(-1\) + b\^2\)\)] + \((\(-\[ImaginaryI]\) + a)\)\ \((4\ \[ImaginaryI]\ a\ b\ \@\(\(-1\ \) + b\^2\)\ \((1 + b - \@\(\(-1\) + b\^2\))\)\^\(\[ImaginaryI]\ a\)\ \((1 + \ b + \@\(\(-1\) + b\^2\))\)\^\(\[ImaginaryI]\ a\)\ AppellF1[2 + \[ImaginaryI]\ a, 2, 2, 3 + \[ImaginaryI]\ a, \(-\(1\/\(b + \@\(\ \(-1\) + b\^2\)\)\)\), 1\/\(\(-b\) + \@\(\(-1\) + b\^2\)\)] - \[ImaginaryI]\ \ \((\(-2\)\ \[ImaginaryI] + a)\)\ \((\((1 + b - \@\(\(-1\) + b\^2\))\)\^\(\ \[ImaginaryI]\ a\)\ \((\(2 + 2\ b\)\/\(1 + b + \@\(\(-1\) + b\^2\)\))\)\^\(\ \[ImaginaryI]\ a\)\ \((1 + b + \@\(\(-1\) + b\^2\))\)\^\(\[ImaginaryI]\ a\)\ \ Hypergeometric2F1[\(-\[ImaginaryI]\)\ a, \(-\[ImaginaryI]\)\ a, 1 - \ \[ImaginaryI]\ a, \(\(-b\) + \@\(\(-1\) + b\^2\)\)\/\(\(-1\) - b + \@\(\(-1\) \ + b\^2\)\)] - \((1 + b - \@\(\(-1\) + b\^2\))\)\^\(\[ImaginaryI]\ a\)\ \ \((\(\(-2\) - 2\ b\)\/\(\(-1\) - b + \@\(\(-1\) + \ b\^2\)\))\)\^\(\[ImaginaryI]\ a\)\ \((1 + b + \@\(\(-1\) + b\^2\))\)\^\(\ \[ImaginaryI]\ a\)\ Hypergeometric2F1[\(-\[ImaginaryI]\)\ a, \(-\[ImaginaryI]\ \)\ a, 1 - \[ImaginaryI]\ a, \(b + \@\(\(-1\) + b\^2\)\)\/\(1 + b + \@\(\(-1\) + \ b\^2\)\)] + \((1 + b + \@\(\(-1\) + b\^2\))\)\^\(\[ImaginaryI]\ a\)\ \ Hypergeometric2F1[\[ImaginaryI]\ a, \[ImaginaryI]\ a, 1 + \[ImaginaryI]\ a, \ \(b - \@\(\(-1\) + b\^2\)\)\/\(1 + b - \@\(\(-1\) + b\^2\)\)] - \((1 + b - \@\ \(\(-1\) + b\^2\))\)\^\(\[ImaginaryI]\ a\)\ Hypergeometric2F1[\[ImaginaryI]\ \ a, \[ImaginaryI]\ a, 1 + \[ImaginaryI]\ a, \(b + \@\(\(-1\) + b\^2\)\)\/\(1 + b + \@\(\(-1\) + b\^2\)\)])\))\))\))\ \))\))\)/\((a\ \((4 + 5\ a\^2 + a\^4)\)\ \@\(\(-1\) + b\^2\))\)\)