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series of exponential

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eerams

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Jan 13, 2003, 6:05:47 AM1/13/03
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Hi,

Does somebody know how to express the following series in terms of
more elemntal functions or any functional form for that matter


Sum exp(-(d/do)^k) Cos[2 Pi d (x-lo)] d=1,...Infinity

k is a positive number, lo is a fixed parameter and x is the free
variable.
Solutions wich involves restrictions on some of the parameters will
also be welcome.

Any answer please send a copy to eer...@yahoo.com

Thanks in advance
EER

Axel Vogt

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Jan 13, 2003, 5:09:50 PM1/13/03
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I do not know whether the following might help. Passing to
integrals you more or less are looking for the value of the
pdf Pareto-Levy function (in a specific point) given here as
int(exp(-(t)^k)* cos(2* Pi *t *z), t=0..infinity).

For z=0 this is GAMMA(1/k)/k. So i have doubts that you can
have an expression through elementary functions in the discrete
case. Hmmm ... ok, may be infinite sums of Newton or Laguerre
polynomials.

Does that help?

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