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Sat 4 Mar, 2006 08:20 am
If somebody knows some hint where to find a useful formula or the fouriertransform of exp (-a*x) devided by (1 + x**N) . x is only .ge. zero a is strictly positve real, N is an positive integer. Actually I need it for N=10. (boundaries zero to infinity)
Complex transform did not work w residues in quarter circle (if I am not mistaken). Semicircle not possible, because integrand explodes for negative x.
The function you describe is measurable and without singolarities on the finite interval you specified. Therefore it has a Fourrier Transform determinablew by the standard integral formula. You could also use a Finite Fourier Transform on any set of numerical values determined by the function.
fouriertransform more precise
i could either calc the following
exp(-ax) *cos( mx)/ (1+ x**N) or go into the complex
and use
exp ( -az) * exp (i*b*z) / (1+ z**N)
then of course i get singularities of z**N = -1 = exp( i*(2k+1)*pi); then a get N singularities at
z= exp( i(2k+1)*pi/N).
the calc of residues in the first quarter circle is simple. however the integrand along the y-axis does not vanish.
of course i could do it numerically but this does not help in this case.
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