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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 ( mod k ) and has the finite Fourier-series expansion
3: 28.2 Definitions and Basic Properties
28.2.18 w ( z ) = n = c 2 n e i ( ν + 2 n ) 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 θ ) ; 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
8: 28.5 Second Solutions fe n , 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 ce n , se n functions, see McLachlan (1947, Chapter VII) or Meixner and Schäfke (1954, §2.72). …
9: 24.8 Series Expansions
§24.8(i) Fourier Series
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 𝖯 .