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

Authors

  • Maha Saeed Algorabi Batterjee Education & Training Academy
  • M.A Sharaf Batterjee Education & Training Academy , Jeddah, Saudi Arabia

DOI:

https://doi.org/10.24297/jam.v12i5.246

Keywords:

Fourier series expansions, fraction and complex powers of sine and cosine, recursive algorithms.

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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Author Biography

M.A Sharaf, Batterjee Education & Training Academy , Jeddah, Saudi Arabia

Department of Mathematics

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Published

2016-06-30

How to Cite

Algorabi, M. S., & Sharaf, M. (2016). Fourier Series Expansions of Powers of the Trigonometric Sine and Cosine Functions. JOURNAL OF ADVANCES IN MATHEMATICS, 12(5), 6248–6253. https://doi.org/10.24297/jam.v12i5.246

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Articles