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Fourier series


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1: 1.8 Fourier Series
§1.8 Fourier Series
Bessel’s Inequality
Uniqueness of Fourier Series
2: 28.14 Fourier Series
§28.14 Fourier Series
The Fourier series
3: 27.17 Other Applications
Reed et al. (1990, pp. 458–470) describes a number-theoretic approach to Fourier analysis (called the arithmetic Fourier transform) that uses the Möbius inversion (27.5.7) to increase efficiency in computing coefficients of Fourier series. …
4: Peter L. Walker
Walker’s books are An Introduction to Complex Analysis, published by Hilger in 1974, The Theory of Fourier Series and Integrals, published by Wiley in 1986, Elliptic Functions. A Constructive Approach, published by Wiley in 1996, and Examples and Theorems in Analysis, published by Springer in 2004. …
5: 6.16 Mathematical Applications
Consider the Fourier seriesCompare Figure 6.16.1. … It occurs with Fourier-series expansions of all piecewise continuous functions. … …
6: 1.15 Summability Methods
§1.15(iii) Summability of Fourier Series
Poisson Kernel
Fejér Kernel
Abel Means
7: 29.20 Methods of Computation
The Fourier series may be summed using Clenshaw’s algorithm; see §3.11(ii). … The corresponding eigenvectors yield the coefficients in the finite Fourier series for Lamé polynomials. …
8: 21.10 Methods of Computation
In addition to evaluating the Fourier series, the main problem here is to compute a Riemann matrix originating from a Riemann surface. …
9: 27.10 Periodic Number-Theoretic Functions
Every function periodic (mod k ) can be expressed as a finite Fourier series of the form … is a periodic function of n ( mod k ) and has the finite Fourier-series expansion …
10: Guide to Searching the DLMF
Table 1: Query Examples
Query Matching records contain
"Fourier transform" and series both the phrase “Fourier transform” and the word “series”.
Fourier or series at least one of the words “Fourier” or “series”.
Fourier (transform or series) at least one of “Fourier transform” or “Fourier series”.