Weber transform
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1—10 of 19 matching pages
1: 10.22 Integrals
2: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions
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►For generalizations see the Weber transform (10.22.78) and an extended Bessel transform (10.22.79).
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3: 10.1 Special Notation
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►For older notations see British Association for the Advancement of Science (1937, pp. xix–xx) and Watson (1944, Chapters 1–3).
4: 2.8 Differential Equations with a Parameter
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►First we apply the Liouville transformation (§1.13(iv)) to (2.8.1).
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►The transformed equation has the form
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►The transformed differential equation is
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►The transformed differential equation is
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►For and see §10.2(ii).
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5: Bibliography N
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On an integral transform involving a class of Mathieu functions.
SIAM J. Math. Anal. 20 (6), pp. 1500–1513.
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On an asymptotic expansion of the Kontorovich-Lebedev transform.
Applicable Anal. 39 (4), pp. 249–263.
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On an asymptotic expansion of the Kontorovich-Lebedev transform.
Methods Appl. Anal. 3 (1), pp. 98–108.
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The resurgence properties of the large order asymptotics of the Anger-Weber function I.
J. Class. Anal. 4 (1), pp. 1–39.
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The resurgence properties of the large order asymptotics of the Anger-Weber function II.
J. Class. Anal. 4 (2), pp. 121–147.
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6: Guide to Searching the DLMF
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Table 1: Query Examples
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Query | Matching records contain |
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"Fourier transform" and series |
both the phrase “Fourier transform” and the word “series”. |
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Fourier (transform or series) |
at least one of “Fourier transform” or “Fourier series”. |
1/(2pi) and "Fourier transform" |
both and the phrase “Fourier transform”. |
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BesselJ_nu and BesselY_nu |
both the Bessel functions and . |
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7: Bibliography S
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The Laplace Transform: Theory and Applications.
Undergraduate Texts in Mathematics, Springer-Verlag, New York.
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Numerical evaluation of the Hankel transform.
Comput. Phys. Comm. 116 (2-3), pp. 278–294.
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On integral representation of Weber’s parabolic cylinder function and its expansion into an infinite series.
J. Indian Math. Soc. (N. S.) 4, pp. 34–38.
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On certain integrals and expansions involving Weber’s parabolic cylinder functions.
J. Indian Math. Soc. (N. S.) 4, pp. 158–166.
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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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8: Bibliography V
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An integral transform involving Heun functions and a related eigenvalue problem.
SIAM J. Math. Anal. 17 (3), pp. 688–703.
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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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Transformations of some Gauss hypergeometric functions.
J. Comput. Appl. Math. 178 (1-2), pp. 473–487.
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Representation of Lie Groups and Special Functions. Volume 1: Simplest Lie Groups, Special Functions and Integral Transforms.
Mathematics and its Applications (Soviet Series), Vol. 72, Kluwer Academic Publishers Group, Dordrecht.
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9: Bibliography Z
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Integrali di funzioni di Anger, Weber ed Airy-Hardy.
Rend. Sem. Mat. Univ. Padova 58, pp. 275–285 (Italian).
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Distribution Theory and Transform Analysis, An Introduction and Generalized Functions with Applications.
Dover, New York.
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Generalized Watson Transforms and Applications to Group Representations.
Ph.D. Thesis, University of Vermont, Burlington,VT.
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A fast Fourier-Bessel transform algorithm.
Zh. Vychisl. Mat. i Mat. Fiz. 35 (7), pp. 1128–1133 (Russian).
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