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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
G. J. O. Jameson*
Affiliation:
13 Sandown Road, Lancaster LA1 4LN e-mail: [email protected]
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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
Information
The Mathematical Gazette , Volume 107 , Issue 570 , November 2023 , pp. 412 - 421
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Copyright
© The Authors, 2023 Published by Cambridge University Press on behalf of The Mathematical Association

References

Jameson, Graham and Lord, Nick, Integrals evaluated in terms of Catalan's constant, Math. Gaz. 101 (March 2017) pp. 38–49.CrossRefGoogle Scholar
Stewart, Seán M., A Catalan constant inspired integral odyssey, Math. Gaz. 104 (November 2020) pp. 449–459.CrossRefGoogle Scholar