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Question: Approximate series solutions for two divergent solutions

Question:Approximate series solutions for two divergent solutions

daljit97 65 Maple
integration series asymptotic elliptic-integral
February 10 2021
0

Hi I am trying to compute the series approximation for the difference between these two divergent integrals

M := int(cosh(p)^2/sqrt(cosh(p)^2 - (1 + x)^2*sinh(p)^2), p = 0 .. 1/2*ln(1/x));

N := int((1 + x)*sinh(p)^2/sqrt(cosh(p)^2 - (1 + x)^2*sinh(p)^2), p = 0 .. 1/2*ln(1/x))

 

where x,p are positive and x is approaching zero. I would like to get a series expansion of M-N, but I am not quite if this is possible.

 
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