Re: An exact 1-D integration challenge - 3
Let
I = int(0,inf){(1-exp(-z))exp(-z/2)/z }dz
and z^(-1) = int(0,inf){exp(-az)}da
So That
I = int(0,inf){ int(0,inf){(1-exp(-z))exp(-z/2)*exp(-az) }dz }da
= int(0,inf){ int(0,inf){exp(-(a+1/2)z ) - exp(-(a+3/2)z )}dz }da
= int(0,inf){ 1/(a+1/2) - 1/(a+3/2) } da
= int(0,inf){ d/da( ln( (a+1/2)/(a+3/2) ) ) }da
= ln( (a+1/2)/(a+3/2) )|a=>inf - ln( (a+1/2)/(a+3/2) )|a=>0
= 0 - ln(1/3)
= - ln(1/3) = 1.098162288668109....
How exact do you need!!!!
Jim Turner
Manager, Business Development
Dynacs Military and Defense
1300 Hercules, Suite 205
Houston, TX 77058
281-226-5213
jturner@dynacsmdi.com
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