Fourier
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21: 28.15 Expansions for Small
§28.15 Expansions for Small
…22: 28.23 Expansions in Series of Bessel Functions
23: 28.34 Methods of Computation
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(d)
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Solution of the systems of linear algebraic equations (28.4.5)–(28.4.8) and (28.14.4), with the conditions (28.4.9)–(28.4.12) and (28.14.5), by boundary-value methods (§3.6) to determine the Fourier coefficients. Subsequently, the Fourier series can be summed with the aid of Clenshaw’s algorithm (§3.11(ii)). See Meixner and Schäfke (1954, §2.87). This procedure can be combined with §28.34(ii)(d).
24: 29.15 Fourier Series and Chebyshev Series
§29.15 Fourier Series and Chebyshev Series
►§29.15(i) Fourier Coefficients
… ►When , , the Fourier series (29.6.1) terminates: … ►When , , the Fourier series (29.6.16) terminates: … ►When , , the Fourier series (29.6.31) terminates: …25: 22.11 Fourier and Hyperbolic Series
§22.11 Fourier and Hyperbolic Series
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22.11.13
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►For further Fourier series see Oberhettinger (1973, pp. 23–27).
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26: 30.15 Signal Analysis
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§30.15(iii) Fourier Transform
… ►Equations (30.15.4) and (30.15.6) show that the functions are -bandlimited, that is, their Fourier transform vanishes outside the interval . …27: 1.17 Integral and Series Representations of the Dirac Delta
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§1.17(ii) Integral Representations
►Formal interchange of the order of integration in the Fourier integral formula ((1.14.1) and (1.14.4)): … ►
1.17.12
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►Formal interchange of the order of summation and integration in the Fourier summation formula ((1.8.3) and (1.8.4)):
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1.17.17
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28: Bibliography O
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Tables of Fourier Transforms and Fourier Transforms of Distributions.
Springer-Verlag, Berlin.
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Fourier Expansions. A Collection of Formulas.
Academic Press, New York-London.
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An error analysis of the modified Clenshaw method for evaluating Chebyshev and Fourier series.
J. Inst. Math. Appl. 20 (3), pp. 379–391.
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29: Bibliography T
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Some definite integrals and Fourier series for Jacobian elliptic functions.
Z. Angew. Math. Mech. 49, pp. 95–96.
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Fourier Analysis on Finite Groups and Applications.
London Mathematical Society Student Texts, Vol. 43, Cambridge University Press, Cambridge.
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Introduction to the Theory of Fourier Integrals.
Third edition, Chelsea Publishing Co., New York.
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Fourier Series.
Prentice-Hall Inc., Englewood Cliffs, N.J..
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