# Euler-Fourier formulas

Formulas for the coefficients of a Fourier series.

If is a function of period defined on the real line and if , then the formulas are:

and

The formal series

and

are both called the Fourier series of . They have the same partial sums:

for all and all . The coefficient is also denoted by .

How to Cite This Entry:
Euler-Fourier formulas. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Euler-Fourier_formulas&oldid=22387