Fabry%20transformation
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1: 1.14 Integral Transforms
§1.14 Integral Transforms
►§1.14(i) Fourier Transform
… ►§1.14(iii) Laplace Transform
… ►Fourier Transform
… ►Laplace Transform
…2: 2.7 Differential Equations
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►To include the point at infinity in the foregoing classification scheme, we transform it into the origin by replacing in (2.7.1) with ; see Olver (1997b, pp. 153–154).
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►See §2.11(v) for other examples.
►The exceptional case is handled by Fabry’s transformation:
…The transformed differential equation either has a regular singularity at , or its characteristic equation has unequal roots.
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3: 20 Theta Functions
Chapter 20 Theta Functions
…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: 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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Reduction and evaluation of elliptic integrals.
Math. Comp. 20 (94), pp. 223–231.
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A table of integrals of the error functions.
J. Res. Nat. Bur. Standards Sect B. 73B, pp. 1–20.
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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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The Laplace Transform.
Princeton Mathematical Series, v. 6, Princeton University Press, Princeton, NJ.
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8: 20.7 Identities
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