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Question: incomplete integral in watson lemma

Question:incomplete integral in watson lemma

brunoroy 0 Maple
integral
April 21 2011
0

Hi,

I would like to apply watson lemma on f(t) = 1/((t+1)*((t/a)-1)), with a a constant, and x tending to infinity.

The problem is that my integral I have to compute is not from 0, but from a....

My integral is : I = int (exp(-x*t)*(t^(λ))*f(t), t=a..∞), with λ>-1, x->∞.

I know that if a=0, and (taylor expansion) f(t) = ∑ b_n*(t^n), n=0..∞, then

I = ∑ b_n*Γ(λ+n+1)/(x^(λ+n+1)), n=0..∞.

Does somebody knows how to do when a≠0 ?

Thank you very much,

Bruno.

 
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