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

Author: Vittorio Massidda
Journal: Math. Comp. 41 (1983), 555-557
MSC: Primary 33A10; Secondary 42A16
MathSciNet review: 717702
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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.

References [Enhancements On Off] (What's this?)

  • [1] M. Abramowitz & I. Stegun, eds., Handbook of Mathematical functions, Dover, New York, 1965.
  • [2] I. S. Gradshteyn & I. M. Ryzhik, Table of Integrals, Series and Products, Academic Press, New York, 1980.
  • [3] G. N. Watson, A treatise on the theory of Bessel functions, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1995. Reprint of the second (1944) edition. MR 1349110

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Keywords: Integrals involving exponential and trigonometric functions, modified Bessel functions, Fourier coefficients
Article copyright: © Copyright 1983 American Mathematical Society

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