Analytical calculation of a class of integrals containing exponential and trigonometric functions
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- by Vittorio Massidda PDF
- Math. Comp. 41 (1983), 555-557 Request permission
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
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M. Abramowitz & I. Stegun, eds., Handbook of Mathematical functions, Dover, New York, 1965.
I. S. Gradshteyn & I. M. Ryzhik, Table of Integrals, Series and Products, Academic Press, New York, 1980.
- 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
Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Math. Comp. 41 (1983), 555-557
- MSC: Primary 33A10; Secondary 42A16
- DOI: https://doi.org/10.1090/S0025-5718-1983-0717702-8
- MathSciNet review: 717702