Fourier-series expansions

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1: 6.16 Mathematical Applications

… ►Compare Figure 6.16.1. … ►It occurs with Fourier-series expansions of all piecewise continuous functions. … …

2: 27.10 Periodic Number-Theoretic Functions

… ►is a periodic function of $n(modk)$ and has the finite Fourier-series expansion …

3: 28.2 Definitions and Basic Properties

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28.2.18 $$w(z)=\sum _{n=-\mathrm{\infty }}^{\mathrm{\infty }}{c}_{2n}{\mathrm{e}}^{\mathrm{i}(\nu +2n)z}$$

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Symbols:

$\mathrm{e}$: base of natural logarithm, $\mathrm{i}$: imaginary unit, $n$: integer, $z$: complex variable, $\nu$: complex parameter, $w(z)$: Mathieu’s equation solution and $c_{2n}$: coefficients

A&S Ref:

20.3.8

Permalink:

http://dlmf.nist.gov/28.2.E18

Encodings:

pMML, png, TeX

See also:

Annotations for §28.2(iv), §28.2 and Ch.28

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4: 1.8 Fourier Series

… ►For collections of Fourier-series expansions see Prudnikov et al. (1986a, v. 1, pp. 725–740), Gradshteyn and Ryzhik (2015, §§1.44–1.45), and Oberhettinger (1973). …

5: 3.11 Approximation Techniques

… ►In fact, (3.11.11) is the Fourier-series expansion of $f(\cos \theta )$; compare (3.11.6) and §1.8(i). …

6: 29.6 Fourier Series

… ►An alternative version of the Fourier series expansion (29.6.1) is given by …

7: 22.11 Fourier and Hyperbolic Series

§22.11 Fourier and Hyperbolic Series

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8: 28.5 Second Solutions ${\mathrm{fe}}_n$, ${\mathrm{ge}}_n$

… ►For further information on $C_n(q)$, $S_n(q)$, and expansions of $f_n(z,q)$, $g_n(z,q)$ in Fourier series or in series of ${\mathrm{ce}}_n$, ${\mathrm{se}}_n$ functions, see McLachlan (1947, Chapter VII) or Meixner and Schäfke (1954, §2.72). …

9: Bibliography V

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On the series expansion method for computing incomplete elliptic integrals of the first and second kinds. Math. Comp. 23 (105), pp. 61–69.

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External Links:

FullText, MathReview, ZentralBlatt

Referenced by:

§19.12, §19.5.

Encodings:

BibTeX

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Computational Frameworks for the Fast Fourier Transform. Frontiers in Applied Mathematics, Vol. 10, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.

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External Links:

ISBN 0-89871-285-8, MathReview (S. Hitotumatu), ZentralBlatt

Referenced by:

§3.11(v).

Encodings:

BibTeX

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An infinite series of Weber’s parabolic cylinder functions. Proc. Benares Math. Soc. (N.S.) 3, pp. 37.

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External Links:

MathReview (M. C. Gray), ZentralBlatt

Referenced by:

§12.13(ii).

Encodings:

BibTeX

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Some novel infinite series of spherical Bessel functions. Quart. Appl. Math. 42 (3), pp. 321–324.

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External Links:

ISSN 0033-569X, MathReview (A. de Castro Brzezicki), ZentralBlatt

Referenced by:

§10.60(iii), §10.60(iii).

Encodings:

BibTeX

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Fourier series representation of Ferrers function $𝖯$ .

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External Links:

FullText

Referenced by:

(14.13.1).

Encodings:

BibTeX

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10: 24.8 Series Expansions

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§24.8(i) Fourier Series

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