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Fourier coefficients of ${1 \over {\sin \,\theta }}$ and ${\theta\over {\sin \,\theta }}$

Published online by Cambridge University Press:  11 October 2023

G. J. O. Jameson*
Affiliation:
13 Sandown Road, Lancaster LA1 4LN e-mail: pgjameson@talktalk.net

Extract

Recall that for a 2π-periodic function f , the Fourier coefficients on the interval (–Π, Π) are

and the Fourier series for f is

Type
Articles
Copyright
© The Authors, 2023 Published by Cambridge University Press on behalf of The Mathematical Association

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References

Jameson, Graham and Lord, Nick, Integrals evaluated in terms of Catalan's constant, Math. Gaz. 101 (March 2017) pp. 3849.CrossRefGoogle Scholar
Stewart, Seán M., A Catalan constant inspired integral odyssey, Math. Gaz. 104 (November 2020) pp. 449459.CrossRefGoogle Scholar