Hi,i am trying to integrate the function exp(-i*r(x)*cos(x)) from -pi to pi,where(adsbygoogle = window.adsbygoogle || []).push({});

r(x)=sqrt(A^2*cos(x)^2+B^2*sin(x)^2),A and B are constant.the function

exp(-i*r(x)*cos(x)) is similar with the function exp(-i*r*cos(x)) which integrate from -pi to pi is 2*pi*BesselJ(0,r).In the function exp(-i*r*cos(x)) , r is constant and usually means radius, but in the function exp(-i*r(x)*cos(x)), r(x) is a variable and define from ellipse.so the constant A can be considered as the major axis of the ellipse ; B the constant can be considered as the short axis of the ellipse.

Can anybody help me? Thank you very much.

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# Integration of the function exp(-i*r(x)*cos(x))

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