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Question: Procedure asymptotic expansion

Question:Procedure asymptotic expansion

Math Pi Euler 30 Maple
asymptotic
February 17 2018
0

Dear all, I've been given the following procedure:

> int_part:=proc(f,h,n::integer) local k,u,v,s;
     > u:=f;
     > v:=h;
     > s:=0;

     > for k from 1 to n do;
     > u:=int(u,t);
     > s:=s-(-1)^(k)*u*v;
     > v:=diff(v,t);

> od;
> s; end: 

To apply on the following function: f:=int((exp(-x*t))/sqrt(t(t+1)),t=1..infinity);

And f is a function of x. F(x).

It should give the asymptotic expansion up to O(x^-6). But probably I do something wrong. Can somebody help me please?

Best wishes, Math
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