# Fourier-series expansions

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## 1—10 of 19 matching pages

##### 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 $n\pmod{k}$ and has the finite Fourier-series expansion
##### 3: 28.2 Definitions and Basic Properties
28.2.18 $w(z)=\sum_{n=-\infty}^{\infty}c_{2n}e^{\mathrm{i}(\nu+2n)z}$
##### 4: 1.8 Fourier Series
For collections of Fourier-series expansions see Prudnikov et al. (1986a, v. 1, pp. 725–740), Gradshteyn and Ryzhik (2000, pp. 45–49), 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 …
##### 8: 28.5 Second Solutions $\operatorname{fe}_{n}$, $\operatorname{ge}_{n}$
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 $\operatorname{ce}_{n}$, $\operatorname{se}_{n}$ functions, see McLachlan (1947, Chapter VII) or Meixner and Schäfke (1954, §2.72). …
##### 10: Bibliography V
• H. Van de Vel (1969) On the series expansion method for computing incomplete elliptic integrals of the first and second kinds. Math. Comp. 23 (105), pp. 61–69.
• C. Van Loan (1992) Computational Frameworks for the Fast Fourier Transform. Frontiers in Applied Mathematics, Vol. 10, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.
• R. S. Varma (1941) An infinite series of Weber’s parabolic cylinder functions. Proc. Benares Math. Soc. (N.S.) 3, pp. 37.
• A. N. Vavreck and W. Thompson (1984) Some novel infinite series of spherical Bessel functions. Quart. Appl. Math. 42 (3), pp. 321–324.
• H. Volkmer (2021) Fourier series representation of Ferrers function ${\sf P}$ .