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2016•JOURNAL OF ADVANCES IN MATHEMATICSOpen access

Fourier Series Expansions of Powers of the Trigonometric Sine and Cosine Functions

Maha Saeed Algorabi, M. A. Sharaf

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Abstract

In this paper, Fourier series expansions of powers of sine and cosine functions are established for any possible power real or complex or positive integer. Recurrence relations are established to facilities the computations of the coefficients of expansions formulae. Numerical applications for real and complex powers are also included , the accuracy of the computed values are at least of order . While the applications for positive integer powers are given as exact analytical expressions.

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What this paper is about

In this paper, Fourier series expansions of powers of sine and cosine functions are established for any possible power real or complex or positive integer. Recurrence relations are established to facilities the computations of the coefficients of expansions formulae. Numerical applications for real and complex powers are also included , the accuracy of the computed values are at least of order . While the applications for positive integer powers are given as exact analytical expressions.

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Available abstract

In this paper, Fourier series expansions of powers of sine and cosine functions are established for any possible power real or complex or positive integer. Recurrence relations are established to facilities the computations of the coefficients of expansions formulae. Numerical applications for real and complex powers are also included , the accuracy of the computed values are at least of order . While the applications for positive integer powers are given as exact analytical expressions.

Key concepts: Mathematics, Sine, Trigonometric functions, Fourier sine and cosine series, Sine and cosine transforms, Fourier series, Series (stratigraphy), Integer (computer science)

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