Stieltjes transforms
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1: 2.6 Distributional Methods
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§2.6(ii) Stieltjes Transform
… ►The Stieltjes transform of is defined by ►
2.6.8
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2.6.25
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►Corresponding results for the generalized
Stieltjes transform
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2: 1.14 Integral Transforms
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: 9.10 Integrals
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§9.10(vii) Stieltjes Transforms
…5: Bibliography N
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On the large argument asymptotics of the Lommel function via Stieltjes transforms.
Asymptot. Anal. 91 (3-4), pp. 265–281.
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6: Bibliography J
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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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7: Errata
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Section 1.14
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There have been extensive changes in the notation used for the integral transforms defined in §1.14. These changes are applied throughout the DLMF. The following table summarizes the changes.
Transform | New | Abbreviated | Old |
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Notation | Notation | Notation | |
Fourier | |||
Fourier Cosine | |||
Fourier Sine | |||
Laplace | |||
Mellin | |||
Hilbert | |||
Stieltjes |
Previously, for the Fourier, Fourier cosine and Fourier sine transforms, either temporary local notations were used or the Fourier integrals were written out explicitly.
8: Bibliography W
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Gevrey asymptotics and Stieltjes transforms of algebraically decaying functions.
Proc. Roy. Soc. London Ser. A 458, pp. 625–644.
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9: Bibliography K
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Fractional integral and generalized Stieltjes transforms for hypergeometric functions as transmutation operators.
SIGMA Symmetry Integrability Geom. Methods Appl. 11, pp. Paper 074, 22.
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10: Bibliography B
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Stieltjes transforms and the Stokes phenomenon.
Proc. Roy. Soc. London Ser. A 429, pp. 227–246.
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