Analytical calculation of a class of integrals containing exponential and trigonometric functions

Abstract:

It is shown how to evaluate analytically integrals from 0 to $2\pi$ of functions of the type $f(\phi )\;g(\phi )\exp \{ G(\phi )\}$, where $g(\phi )$ and $G(\phi )$ are linear combinations of powers of $\sin \phi$ and $\cos \phi$, and $f(\phi )$ is such that its Fourier coefficients can be evaluated analytically. The result is expressed in terms of modified Bessel functions.