Fourier%20series
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1: Bibliography O
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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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2: Peter L. Walker
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►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.
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3: 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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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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An infinite series of Weber’s parabolic cylinder functions.
Proc. Benares Math. Soc. (N.S.) 3, pp. 37.
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Error estimates for Rayleigh-Ritz approximations of eigenvalues and eigenfunctions of the Mathieu and spheroidal wave equation.
Constr. Approx. 20 (1), pp. 39–54.
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Fourier series representation of Ferrers function
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4: Bibliography R
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On the definition and properties of generalized - symbols.
J. Math. Phys. 20 (12), pp. 2398–2415.
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Remark on Algorithm 498: Airy functions using Chebyshev series approximations.
ACM Trans. Math. Software 7 (3), pp. 404–405.
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Fourier analysis and signal processing by use of the Möbius inversion formula.
IEEE Trans. Acoustics, Speech, Signal Processing 38, pp. 458–470.
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Methods of Modern Mathematical Physics, Vol. 2, Fourier Analysis, Self-Adjointness.
Academic Press, New York.
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Elliptic hypergeometric series on root systems.
Adv. Math. 181 (2), pp. 417–447.
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5: 6.16 Mathematical Applications
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►Consider the Fourier series
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►Compare Figure 6.16.1.
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►It occurs with Fourier-series expansions of all piecewise continuous functions.
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6: Bibliography F
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Un théorème de Paley-Wiener pour la transformation de Fourier sur un espace riemannien symétrique de rang un.
J. Funct. Anal. 49 (2), pp. 230–268.
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Sur certaines sommes des intégral-cosinus.
Bull. Soc. Math. Phys. Serbie 12, pp. 13–20 (French).
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Studies on Divergent Series and Summability & The Asymptotic Developments of Functions Defined by Maclaurin Series.
Chelsea Publishing Co., New York.
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Series expansions of symmetric elliptic integrals.
Math. Comp. 81 (278), pp. 957–990.
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7: Bibliography C
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An algorithm for the Fourier-Bessel transform.
Comput. Phys. Comm. 23 (4), pp. 343–353.
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Introduction to the Theory of Fourier’s Series and Integrals.
3rd edition, Macmillan, London.
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Macdonald’s evaluation conjectures and difference Fourier transform.
Invent. Math. 122 (1), pp. 119–145.
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A method for numerical calculation of Fourier integrals.
Numer. Math. 8 (5), pp. 422–436.
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An algorithm for the machine calculation of complex Fourier series.
Math. Comp. 19 (90), pp. 297–301.
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8: Bibliography S
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Numerical evaluation of spherical Bessel transforms via fast Fourier transforms.
J. Comput. Phys. 100 (2), pp. 294–296.
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Uniform asymptotic forms of modified Mathieu functions.
Quart. J. Mech. Appl. Math. 20 (3), pp. 365–380.
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Numerical Methods Based on Sinc and Analytic Functions.
Springer Series in Computational Mathematics, Vol. 20, Springer-Verlag, New York.
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A Guide to Distribution Theory and Fourier Transforms.
Studies in Advanced Mathematics, CRC Press, Boca Raton, FL.
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An Introduction to Basic Fourier Series.
Developments in Mathematics, Vol. 9, Kluwer Academic Publishers, Dordrecht.
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9: Bibliography K
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Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library.
ACM Trans. Math. Software 20 (4), pp. 447–459.
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Methods of computing the Riemann zeta-function and some generalizations of it.
USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.
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Fourier Analysis.
2nd edition, Cambridge University Press, Cambridge.
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HYP and HYPQ. Mathematica packages for the manipulation of binomial sums and hypergeometric series respectively -binomial sums and basic hypergeometric series.
Séminaire Lotharingien de Combinatoire 30, pp. 61–76.
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A Handbook of Methods of Approximate Fourier Transformation and Inversion of the Laplace Transformation.
Mir, Moscow.
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10: Bibliography B
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Pionic atoms.
Annual Review of Nuclear and Particle Science 20, pp. 467–508.
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Coulomb functions (negative energies).
Comput. Phys. Comm. 20 (3), pp. 447–458.
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A short table of the functions , from to
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Phil. Mag. Series 7 20, pp. 343–347.
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Some solutions of the problem of forced convection.
Philos. Mag. Series 7 20, pp. 322–343.
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From Klein to Painlevé via Fourier, Laplace and Jimbo.
Proc. London Math. Soc. (3) 90 (1), pp. 167–208.
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