Mellin%20transform
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1: 1.14 Integral Transforms
§1.14 Integral Transforms
… ►§1.14(iv) Mellin Transform
… ►Inversion
… ►Parseval-type Formulas
… ►Convolution
…2: 2.5 Mellin Transform Methods
§2.5 Mellin Transform Methods
… ►The Mellin transform of is defined by …The inversion formula is given by … ► … ►To apply the Mellin transform method outlined in §2.5(i), we require the transforms and to have a common strip of analyticity. …3: 15.14 Integrals
§15.14 Integrals
►The Mellin transform of the hypergeometric function of negative argument is given by … ►Laplace transforms of hypergeometric functions are given in Erdélyi et al. (1954a, §4.21), Oberhettinger and Badii (1973, §1.19), and Prudnikov et al. (1992a, §3.37). …Mellin transforms of hypergeometric functions are given in Erdélyi et al. (1954a, §6.9), Oberhettinger (1974, §1.15), and Marichev (1983, pp. 288–299). Inverse Mellin transforms are given in Erdélyi et al. (1954a, §7.5). …4: 20.10 Integrals
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§20.10(i) Mellin Transforms with respect to the Lattice Parameter
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20.10.1
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20.10.2
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20.10.3
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§20.10(ii) Laplace Transforms with respect to the Lattice Parameter
…5: 2.6 Distributional Methods
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§2.6(ii) Stieltjes Transform
… ►The Stieltjes transform of is defined by … ► being the Mellin transform of or its analytic continuation (§2.5(ii)). … ►Corresponding results for the generalized Stieltjes transform … ►where is the Mellin transform of or its analytic continuation. …6: Bibliography F
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Sur certaines sommes des intégral-cosinus.
Bull. Soc. Math. Phys. Serbie 12, pp. 13–20 (French).
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Tables of Elliptic Integrals of the First, Second, and Third Kind.
Technical report
Technical Report ARL 64-232, Aerospace Research Laboratories, Wright-Patterson Air Force Base, Ohio.
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On the asymptotic expansion of Mellin transforms.
SIAM J. Math. Anal. 18 (1), pp. 273–282.
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On weighted polynomial approximation on the whole real axis.
Acta Math. Acad. Sci. Hungar. 20, pp. 223–225.
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7: Bibliography W
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The Nahm equations, finite-gap potentials and Lamé functions.
J. Phys. A 20 (10), pp. 2679–2683.
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The cubic transformation of the hypergeometric function.
Quart. J. Pure and Applied Math. 41, pp. 70–79.
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Some transformations of generalized hypergeometric series.
Proc. London Math. Soc. (2) 26 (2), pp. 257–272.
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The Airy transform.
Amer. Math. Monthly 86 (4), pp. 271–277.
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Explicit error terms for asymptotic expansions of Mellin convolutions.
J. Math. Anal. Appl. 72 (2), pp. 740–756.
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8: Bibliography P
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Asymptotics and Mellin-Barnes Integrals.
Cambridge University Press, Cambridge.
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Smoothing of the Stokes phenomenon using Mellin-Barnes integrals.
J. Comput. Appl. Math. 41 (1-2), pp. 117–133.
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Bounds for ratios of modified Bessel functions.
Integral Transform. Spec. Funct. 9 (4), pp. 293–298.
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Automatic computation of Bessel function integrals.
Comput. Phys. Comm. 25 (3), pp. 289–295.
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Fourier Series and Integral Transforms.
Cambridge University Press, Cambridge.
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9: 13.23 Integrals
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§13.23(i) Laplace and Mellin Transforms
… ►For additional Laplace and Mellin transforms see Erdélyi et al. (1954a, §§4.22, 5.20, 6.9, 7.5), Marichev (1983, pp. 283–287), Oberhettinger and Badii (1973, §1.17), Oberhettinger (1974, §§1.13, 2.8), and Prudnikov et al. (1992a, §§3.34, 3.35). … ►§13.23(ii) Fourier Transforms
… ►§13.23(iii) Hankel Transforms
… ► …10: Bibliography O
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Tables of Lebedev, Mehler and Generalized Mehler Transforms.
Mathematical Note
Technical Report 246, Boeing Scientific Research Lab, Seattle.
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Tables of Fourier Transforms and Fourier Transforms of Distributions.
Springer-Verlag, Berlin.
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Tables of Bessel Transforms.
Springer-Verlag, Berlin-New York.
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Tables of Mellin Transforms.
Springer-Verlag, Berlin-New York.
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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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