Stieltjes transform
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11—17 of 17 matching pages
11: Bibliography M
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Explicit error terms for asymptotic expansions of Stieltjes transforms.
J. Inst. Math. Appl. 22 (2), pp. 129–145.
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12: Bibliography
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Solitons and the Inverse Scattering Transform.
SIAM Studies in Applied Mathematics, Vol. 4, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.
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Lectures on Integral Transforms.
Translations of Mathematical Monographs, Vol. 70, American Mathematical Society, Providence, RI.
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Zeros of Stieltjes and Van Vleck polynomials and applications.
J. Math. Anal. Appl. 110 (2), pp. 327–339.
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Zeros of Stieltjes and Van Vleck polynomials.
Trans. Amer. Math. Soc. 252, pp. 197–204.
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Summations and transformations for basic Appell series.
J. London Math. Soc. (2) 4, pp. 618–622.
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13: 1.16 Distributions
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§1.16(vii) Fourier Transforms of Tempered Distributions
… ►Then its Fourier transform is … ►The Fourier transform of a tempered distribution is again a tempered distribution, and … ►§1.16(viii) Fourier Transforms of Special Distributions
… ►See Hildebrandt (1938) and Chihara (1978, Chapter II) for Stieltjes measures which are used in §18.39(iii); see also Shohat and Tamarkin (1970, Chapter II). …14: 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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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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Expansions in products of Heine-Stieltjes polynomials.
Constr. Approx. 15 (4), pp. 467–480.
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15: Bibliography C
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A quadrature formula for the Hankel transform.
Numer. Algorithms 9 (2), pp. 343–354.
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An algorithm for the Fourier-Bessel transform.
Comput. Phys. Comm. 23 (4), pp. 343–353.
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Quadratic transformations of Appell functions.
SIAM J. Math. Anal. 7 (2), pp. 291–304.
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On Stieltjes’ continued fraction for the gamma function.
Math. Comp. 34 (150), pp. 547–551.
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Optimized fast Hankel transform filters.
Geophysical Prospecting 38 (5), pp. 545–568.
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16: Bibliography H
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The Laplace transform for expressions that contain a probability function.
Bul. Akad. Štiince RSS Moldoven. 1973 (2), pp. 78–80, 93 (Russian).
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A fast FFT-based discrete Legendre transform.
IMA J. Numer. Anal. 36 (4), pp. 1670–1684.
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Asymptotic expansion of Laplace transforms near the origin.
SIAM J. Math. Anal. 1 (1), pp. 118–130.
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Fast Hankel transform algorithm.
IEEE Trans. Acoust. Speech Signal Process. 32 (3), pp. 666–671.
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Definitions of Stieltjes Integrals of the Riemann Type.
Amer. Math. Monthly 45 (5), pp. 265–278.
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17: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions
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►For a Lebesgue–Stieltjes measure on let be the space of all Lebesgue–Stieltjes measurable complex-valued functions on which are square integrable with respect to ,
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►(1.18.57) is the Hankel transform (10.22.76)–(10.22.77).
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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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►Integral transforms (10.22.78) and (10.22.79) are examples of the utility of these extensions.
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