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Question: difficult integral

Question:difficult integral

J F Ogilvie 258 Maple
integration
July 18 2019
1

A research paper published in 1929 claimed that this integral was solved in 1896.

int(exp(I*m*omega + I*b*cos(omega) ),omega=0..2*Pi)           (m integer,  b positive constant)

but it defeats Maple (and other).  Can anybody suggest a way to solve this integral with Maple?
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