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Question: Asymptotic expansions of big integrals

Question:Asymptotic expansions of big integrals

Andrew Carmichael 216 Maple
May 18 2008
0
Dear All, I'm trying to make an asymptotic expansion of the following integral: A := m-> (x-sqrt(x^2+2*x*m+m^2-1))/(sqrt(x)*sqrt(x^2+2*x*m+m^2-1)) ; IntegralA := m-> evalf(Int(A(x, m), x = 0 .. infinity)) ; and similarly for two others P3 := m-> -(-1+4*x^2*m^2+8*x^3*m+2*x*m-3*x^2+m^2)/((2*x^2+1+2*sqrt((x+m)^2/((x+m+1)*(x+m-1)))*x^2)*(x+m+1)*(x+m-1)*sqrt(x)) ; IntegralP3:=m->evalf(Int(P3(x,m)/2,x=0..infinity)); and lastly P1:=(x,m)->sqrt(x)/(sqrt((x+m)^2-1)*(x+m+sqrt((x+m)^2-1))); IntegralP1:=m->evalf(Int(P1(x,1),x=0..infinity)); I need the series asymptotic expansions for large m. Does anybody have any suggestions? Andrew
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