Fourier sine and cosine series

In mathematics, particularly the field of calculus and Fourier analysis, the Fourier sine and cosine series are two mathematical series named after Joseph Fourier. == Notation == In this article, f denotes a real-valued function on R {\displaystyle \mathbb {R} } which is periodic with period 2L. == Sine series == If f is an odd function with period 2 L {\displaystyle 2L} , then the Fourier Half Range sine series of f is defined to be f ( x ) = ∑ n = 1 ∞ b n sin ⁡ ( n π x L ) {\displaystyle f(x)=\sum _{n=1}^{\infty }b_{n}\sin \left({\frac {n\pi x}{L}}\right)} which is just a form of complete Fourier series with the only difference that a 0 {\displaystyle a_{0}} and a n {\displaystyle a_{n}} are zero, and the series is defined for half of the interval.

Source: Wikipedia — Fourier sine and cosine series (CC BY-SA 4.0)

Fourier sine and cosine series

In mathematics, particularly the field of calculus and Fourier analysis, the Fourier sine and cosine series are two mathematical series named after Joseph Fourier. == Notation == In this article, f denotes a real-valued function on R {\displaystyle \mathbb {R} } which is periodic with period 2L. == Sine series == If f is an odd function with period 2 L {\displaystyle 2L} , then the Fourier Half Range sine series of f is defined to be f ( x ) = ∑ n = 1 ∞ b n sin ⁡ ( n π x L ) {\displaystyle f(x)=\sum _{n=1}^{\infty }b_{n}\sin \left({\frac {n\pi x}{L}}\right)} which is just a form of complete Fourier series with the only difference that a 0 {\displaystyle a_{0}} and a n {\displaystyle a_{n}} are zero, and the series is defined for half of the interval.

Source: Wikipedia "Fourier sine and cosine series" · CC BY-SA 4.0

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