Trigonometric series
Encyclopedia
In mathematics
, a trigonometric series is any series
of the form:
It is called a Fourier series
when the terms
and 
have the form:
where
is an integrable function.
Not every trigonometric series is a Fourier Series.
A particular question of interest is: given a trigonometric series, for which values of x does the series converge?
Further reading: Fourier series
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, a trigonometric series is any series
Series (mathematics)
A series is the sum of the terms of a sequence. Finite sequences and series have defined first and last terms, whereas infinite sequences and series continue indefinitely....
of the form:
It is called a Fourier series
Fourier series
In mathematics, a Fourier series decomposes periodic functions or periodic signals into the sum of a set of simple oscillating functions, namely sines and cosines...
when the terms
and have the form:where
is an integrable function.Not every trigonometric series is a Fourier Series.
A particular question of interest is: given a trigonometric series, for which values of x does the series converge?
Further reading: Fourier series
Fourier series
In mathematics, a Fourier series decomposes periodic functions or periodic signals into the sum of a set of simple oscillating functions, namely sines and cosines...