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

Maha Saeed Algorabi | Zendy; M. A. Sharaf | Zendy

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

Author(s) -

Maha Saeed Algorabi,

M. A. Sharaf

Publication year - 2016

Publication title -

journal of advances in mathematics

Language(s) - English

Resource type - Journals

ISSN - 2347-1921

DOI - 10.24297/jam.v12i5.246

Subject(s) - mathematics , sine , trigonometric functions , fourier sine and cosine series , sine and cosine transforms , fourier series , series (stratigraphy) , integer (computer science) , power series , trigonometric integral , inverse trigonometric functions , trigonometric series , computation , mathematical analysis , series expansion , fourier transform , trigonometric substitution , fourier analysis , algorithm , fractional fourier transform , geometry , polynomial , linear interpolation , bicubic interpolation , paleontology , computer science , biology , programming language

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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