Fourier sine and cosine series
In this article, f denotes a real valued function on which is periodic with period 2L.
If f(x) is an odd function, then the Fourier sine series of f is defined to be
If f(x) is an even function, then the Fourier cosine series is defined to be
This notion can be generalized to functions which are not even or odd, but then the above formulas will look different.
- Byerly, William Elwood (1893). "Chapter 2: Development in Trigonometric Series". An Elementary Treatise on Fourier's Series: And Spherical, Cylindrical, and Ellipsoidal Harmonics, with Applications to Problems in Mathematical Physics (2 ed.). Ginn. p. 30.
- Carslaw, Horatio Scott (1921). "Chapter 7: Fourier's Series". Introduction to the Theory of Fourier's Series and Integrals, Volume 1 (2 ed.). Macmillan and Company. p. 196.