Definition of Fourier series in English:

Fourier series

nounˈfʊrɪə

Mathematics

An infinite series of trigonometric functions which represents an expansion or approximation of a periodic function, used in Fourier analysis.
〔数〕傅里叶级数
Example sentencesExamples
- From this he was able to prove that if a function was representable by a trigonometric series then this series is necessarily its Fourier series.
- He carried out many important and fruitful investigations in number theory, in the theory of Bessel functions and of Fourier series, in ordinary and partial differential equations, and in analytical mechanics and potential theory.
- His work led him to study the acceleration of convergence of Fourier series and the approximate solutions to differential equations.
- In mathematics he worked on the calculus of variations, Fourier series, function spaces, Hamiltonian geometrical optics, Schrödinger wave mechanics, and relativity.
- Hardy's interests covered many topics of pure mathematics - Diophantine analysis, summation of divergent series, Fourier series, the Riemann zeta function, and the distribution of primes.

Definition of Fourier series in US English:

Fourier series

noun

Mathematics

An infinite series of trigonometric functions which represents an expansion or approximation of a periodic function, used in Fourier analysis.
〔数〕傅里叶级数
Example sentencesExamples
- In mathematics he worked on the calculus of variations, Fourier series, function spaces, Hamiltonian geometrical optics, Schrödinger wave mechanics, and relativity.
- Hardy's interests covered many topics of pure mathematics - Diophantine analysis, summation of divergent series, Fourier series, the Riemann zeta function, and the distribution of primes.
- From this he was able to prove that if a function was representable by a trigonometric series then this series is necessarily its Fourier series.
- His work led him to study the acceleration of convergence of Fourier series and the approximate solutions to differential equations.
- He carried out many important and fruitful investigations in number theory, in the theory of Bessel functions and of Fourier series, in ordinary and partial differential equations, and in analytical mechanics and potential theory.

词汇	Fourier series
释义	Definition of Fourier series in English: Fourier series nounˈfʊrɪə Mathematics An infinite series of trigonometric functions which represents an expansion or approximation of a periodic function, used in Fourier analysis. 〔数〕傅里叶级数 Example sentencesExamples From this he was able to prove that if a function was representable by a trigonometric series then this series is necessarily its Fourier series. He carried out many important and fruitful investigations in number theory, in the theory of Bessel functions and of Fourier series, in ordinary and partial differential equations, and in analytical mechanics and potential theory. His work led him to study the acceleration of convergence of Fourier series and the approximate solutions to differential equations. In mathematics he worked on the calculus of variations, Fourier series, function spaces, Hamiltonian geometrical optics, Schrödinger wave mechanics, and relativity. Hardy's interests covered many topics of pure mathematics - Diophantine analysis, summation of divergent series, Fourier series, the Riemann zeta function, and the distribution of primes. Definition of Fourier series in US English: Fourier series noun Mathematics An infinite series of trigonometric functions which represents an expansion or approximation of a periodic function, used in Fourier analysis. 〔数〕傅里叶级数 Example sentencesExamples In mathematics he worked on the calculus of variations, Fourier series, function spaces, Hamiltonian geometrical optics, Schrödinger wave mechanics, and relativity. Hardy's interests covered many topics of pure mathematics - Diophantine analysis, summation of divergent series, Fourier series, the Riemann zeta function, and the distribution of primes. From this he was able to prove that if a function was representable by a trigonometric series then this series is necessarily its Fourier series. His work led him to study the acceleration of convergence of Fourier series and the approximate solutions to differential equations. He carried out many important and fruitful investigations in number theory, in the theory of Bessel functions and of Fourier series, in ordinary and partial differential equations, and in analytical mechanics and potential theory.
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