Saturday, November 5, 2016

complex analysis - A definite integral of the exponential of cos

During some calculs, I came across the following definite integral,
2π0sin2θ1+bcosθexp(acosθ)dθ
with a and b constants. I tried to look it up in the Gradshteyn and Ryzhik, for example in Section 3.93: Trigonometric and exponential functions of trigonometric functions, but find nothing helpful. I also tried the Poisson Integral via complex analyse, apparently the exponential function is a little particular, if it's a log function instead of exp that's done, but with exponential I have not yet found the solution.



Thanks in advance if anyone has any idea :)

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