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Re: Calculating a simple integral

• To: mathgroup at smc.vnet.net
• Subject: [mg131078] Re: Calculating a simple integral
• From: Dmitry Smirnov <dsmirnov90 at gmail.com>
• Date: Mon, 10 Jun 2013 04:10:03 -0400 (EDT)
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• References: <20130609083209.86C8769D8@smc.vnet.net> <8984F0D9-AD1E-4ECB-914A-1E3E88498517@mimuw.edu.pl>

I believe that oscillating function as (Cos[z]-1) allows one to calculate
this integral by the residues. Anyway you can check numerically that the
correct answer is following:

-1/32/((kr^2 + 4*Pi^2)^3*kr^5*Pi^3)*(192*Pi^6*Sinh[kr] +
   16*Pi^4*Sinh[kr]*kr^3 + 64*Pi^6*Sinh[kr]*kr - 192*Pi^6*Cosh[kr] -
   112*Pi^4*Cosh[kr]*kr^2 + 112*Pi^4*Sinh[kr]*kr^2 -
   16*Pi^4*Cosh[kr]*kr^3 - 64*Pi^6*Cosh[kr]*kr + 192*Pi^6 - 3*kr^7 -
   28*kr^5*Pi^2 - 96*kr^3*Pi^4 - 128*kr*Pi^6 + 112*kr^2*Pi^4)

• References:
  • Calculating a simple integral
    • From: dsmirnov90@gmail.com