Re: an Integrate question

*To*: mathgroup at smc.vnet.net*Subject*: [mg58918] Re: an Integrate question*From*: "Drago Ganic" <drago.ganic at in2.hr>*Date*: Sat, 23 Jul 2005 05:32:52 -0400 (EDT)*References*: <dbie3r$brm$1@smc.vnet.net><dbkkiq$s49$1@smc.vnet.net> <dbninb$hlj$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Antonio, We have a more precise analytical solution in Mathematica 5.2 than in 5.1. Here is the solution I got with 5.2: In[3]:= Integrate[E^(I*h*x)/(E^(m*Sqrt[k2 + x2])* (Abs[x] + Sqrt[k2 + x2])), {x, 0, Infinity}] Out[3]= Piecewise[{{((1/2)*(2*Gamma[0, (-I)*h*Sqrt[k2 + x2]] - 2*Log[(-I)*h] + 2*Log[(-I)*h*Sqrt[k2 + x2]] - Log[k2 + x2]))/E^((I*h + m)*Sqrt[k2 + x2]), Im[h] > 0}, {(Pi*MeijerG[{{0}, {1/2}}, {{0, 0}, {1/2}}, I*h*Sqrt[k2 + x2]])/E^(m*Sqrt[k2 + x2]), h \[Element] Reals && Im[h] <= 0}}, Integrate[E^(I*h*x - m*Sqrt[k2 + x2])/ (Abs[x] + Sqrt[k2 + x2]), {x, 0, Infinity}, Assumptions -> h \[NotElement] Reals && Im[h] <= 0]] and using assumptions we get just one solution: In[6]:= Assuming[{h, m} \[Element] Reals && Re[k2] <= 0), Integrate[E^(I*h*x)/(E^(m*Sqrt[x2 + k2])*(Abs[x] + Sqrt[x2 + k2])), {x, 0, Infinity}]] Out[6]= (Pi*MeijerG[{{0}, {1/2}}, {{0, 0}, {1/2}}, I*h*Sqrt[k2 + x2]])/E^(m*Sqrt[k2 + x2]) I did not verify the solution. But I don't understand the condition: h \[Element] Reals && Im[h] <= 0 because h \[Element] => Im[h] == 0 ?!? Your case should be covered with the solution given. Gretings, Drago Ganic "Antonio Carlos Siqueira" <acsl at dee.ufrj.br> wrote in message news:dbninb$hlj$1 at smc.vnet.net... > Dear Mathgroup > First of all thanks to Carl Woll and Andreas Dieckman for providing the > answer to the integral. Digging my results a little bit I found > myself with a little different integral. I am trying to calculate some > electromagnetic field in conductive soil, the integral looks like this: > Integrate[Exp[-m Sqrt[x2+k2]]*> Exp[I h > x]/(Abs[x]+Sqrt[x2+k2]),{x,0,Infinity}] > where h and m are real and k is either pure imaginary or has a negative > real part. > Any ideas on how to solve such integral analytically? > After some tests I believe this integral is a job for NIntegrate, > nevertheless it is worth asking if anyone knows any trick to transform > this integral in something that can be solved analytically. > Nice Regards > Antonio >

**Follow-Ups**:**Re: Re: an Integrate question***From:*Pratik Desai <pdesai1@umbc.edu>