Hankel transforms

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1: 15.14 Integrals

… ►Hankel transforms of hypergeometric functions are given in Oberhettinger (1972, §1.17) and Erdélyi et al. (1954b, §8.17). …

2: 10.74 Methods of Computation

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Hankel Transform

… ►The spherical Bessel transform is the Hankel transform (10.22.76) in the case when $\nu$ is half an odd positive integer. …

3: 10.1 Special Notation

… ►For older notations see British Association for the Advancement of Science (1937, pp. xix–xx) and Watson (1944, Chapters 1–3).

4: 13.10 Integrals

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§13.10(v) Hankel Transforms

… ►For additional Hankel transforms and also other Bessel transforms see Erdélyi et al. (1954b, §8.18) and Oberhettinger (1972, §§1.16 and 3.4.42–46, 4.4.45–47, 5.94–97). …

5: 13.23 Integrals

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§13.23(iii) Hankel Transforms

… ►For additional Hankel transforms and also other Bessel transforms see Erdélyi et al. (1954b, §8.18) and Oberhettinger (1972, §1.16 and 3.4.42–46, 4.4.45–47, 5.94–97). …

6: Bibliography W

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Algorithm 794: Numerical Hankel transform by the Fortran program HANKEL. ACM Trans. Math. Software 25 (2), pp. 240–250.

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Notes:

Double-precision Fortran, maximum accuracy 10S.

External Links:

ISSN 0098-3500, Document, GAMS (module 794; package TOMS), ZentralBlatt

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7th item, 10th item.

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Error bounds for asymptotic expansions of Hankel transforms. SIAM J. Math. Anal. 7 (6), pp. 799–808.

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ISSN 1095-7154, Document, MathReview (John S. Lew), ZentralBlatt

Referenced by:

§10.22(v).

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Asymptotic expansions of Hankel transforms of functions with logarithmic singularities. Comput. Math. Appl. 3 (4), pp. 271–286.

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ISSN 0886-9561, Document, MathReview, ZentralBlatt

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§10.22(v).

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7: Bibliography F

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Numerical calculation of singular integrals related to Hankel transform. Comput. Math. Appl. 21 (2-3), pp. 87–94.

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Notes:

Fortran, minimum precision 6D.

External Links:

ISSN 0898-1221, Document, MathReview, ZentralBlatt

Referenced by:

§10.77(ix).

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A note on asymptotic evaluation of some Hankel transforms. Math. Comp. 45 (172), pp. 537–548.

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ISSN 0025-5718, FullText, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§10.22(v), §18.15(i), §18.16(ii).

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8: Bibliography C

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A quadrature formula for the Hankel transform. Numer. Algorithms 9 (2), pp. 343–354.

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ISSN 1017-1398, Document, MathReview (V. I. Polovinkin), ZentralBlatt

Referenced by:

§10.74(vii).

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Numerical integration of related Hankel transforms by quadrature and continued fraction expansion. Geophysics 48 (12), pp. 1671–1686.

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Notes:

Fortran code.

External Links:

ISSN 0098-3500, Document

Referenced by:

§10.77(ix).

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Optimized fast Hankel transform filters. Geophysical Prospecting 38 (5), pp. 545–568.

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Document

Referenced by:

§10.74(vii).

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Computation of Hankel transforms. SIAM Rev. 14 (2), pp. 278–285.

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External Links:

ISSN 1095-7200, Document, MathReview (R. D. Riess), ZentralBlatt

Referenced by:

§10.74(vii).

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BibTeX

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9: Bibliography J

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Fast Hankel transforms. Geophysical Prospecting 27 (4), pp. 876–901.

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External Links:

Document

Referenced by:

§10.74(vii).

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10: 10.22 Integrals

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§10.22(v) Hankel Transform

►The Hankel transform (or Bessel transform) of a function $f(x)$ is defined as … ►For asymptotic expansions of Hankel transforms see Wong (1976, 1977), Frenzen and Wong (1985a) and Galapon and Martinez (2014). ►For collections of Hankel transforms see Erdélyi et al. (1954b, Chapter 8) and Oberhettinger (1972). ►The following two formulas are generalizations of the Hankel transform. …