Airy transform
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1—10 of 28 matching pages
1: 9.10 Integrals
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§9.10(v) Laplace Transforms
… ►§9.10(vi) Mellin Transform
… ►§9.10(vii) Stieltjes Transforms
… ►§9.10(ix) Compendia
►For further integrals, including the Airy transform, see §9.11(iv), Widder (1979), Prudnikov et al. (1990, §1.8.1), Prudnikov et al. (1992a, pp. 405–413), Prudnikov et al. (1992b, §4.3.25), Vallée and Soares (2010, Chapters 3, 4).2: Bibliography W
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The Airy transform.
Amer. Math. Monthly 86 (4), pp. 271–277.
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3: 9.17 Methods of Computation
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►Among the integral representations of the Airy functions the Stieltjes transform (9.10.18) furnishes a way of computing in the complex plane, once values of this function can be generated on the positive real axis.
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4: Bibliography G
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Problem 72-21, Laplace transforms of Airy functions.
SIAM Rev. 15 (4), pp. 796–798.
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5: Bibliography S
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The Laplace transforms of products of Airy functions.
Dirāsāt Ser. B Pure Appl. Sci. 19 (2), pp. 7–11.
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6: 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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►For and see §9.2.
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►of smallest absolute value, and define the envelopes of and by
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7: 9.12 Scorer Functions
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9.12.24
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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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Airy Functions and Applications to Physics.
Second edition, Imperial College Press, London.
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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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Symbolic evaluation of coefficients in Airy-type asymptotic expansions.
J. Math. Anal. Appl. 269 (1), pp. 317–331.
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Transformations of some Gauss hypergeometric functions.
J. Comput. Appl. Math. 178 (1-2), pp. 473–487.
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9: Bibliography P
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A Kummer-type transformation for a hypergeometric function.
J. Comput. Appl. Math. 173 (2), pp. 379–382.
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Bounds for ratios of modified Bessel functions.
Integral Transform. Spec. Funct. 9 (4), pp. 293–298.
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Fourier Series and Integral Transforms.
Cambridge University Press, Cambridge.
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Inequalities for the zeros of the Airy functions.
SIAM J. Math. Anal. 22 (1), pp. 260–267.
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Algorithm 498: Airy functions using Chebyshev series approximations.
ACM Trans. Math. Software 1 (4), pp. 372–379.
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10: Bibliography J
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Numerical calculation of Bessel, Hankel and Airy functions.
Computer Physics Communications 183 (3), pp. 506–519.
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A note on sampling expansion for a transform with parabolic cylinder kernel.
Inform. Sci. 26 (2), pp. 155–158.
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Fast Hankel transforms.
Geophysical Prospecting 27 (4), pp. 876–901.
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Asymptotic behavior of the continued fraction coefficients of a class of Stieltjes transforms including the Binet function.
In Orthogonal functions, moment theory, and continued fractions
(Campinas, 1996),
Lecture Notes in Pure and Appl. Math., Vol. 199, pp. 257–274.
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