Hankel integrals

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1: 10.76 Approximations

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§10.76(ii) Bessel Functions, Hankel Functions, and Modified Bessel Functions

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2: 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).

3: 13.10 Integrals

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§13.10(v) Hankel Transforms

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4: 13.23 Integrals

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§13.23(iii) Hankel Transforms

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5: 10.9 Integral Representations

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Mehler–Sonine and Related Integrals

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Schläfli–Sommerfeld Integrals

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Hankel’s Integrals

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§10.9(iv) Compendia

►For collections of integral representations of Bessel and Hankel functions see Erdélyi et al. (1953b, §§7.3 and 7.12), Erdélyi et al. (1954a, pp. 43–48, 51–60, 99–105, 108–115, 123–124, 272–276, and 356–357), Gröbner and Hofreiter (1950, pp. 189–192), Marichev (1983, pp. 191–192 and 196–210), Magnus et al. (1966, §3.6), and Watson (1944, Chapter 6).

6: 5.9 Integral Representations

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Hankel’s Loop Integral

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Figure 5.9.1: $t$-plane. Contour for Hankel’s loop integral. Magnify

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7: Bibliography G

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Exactification of the Poincaré asymptotic expansion of the Hankel integral: spectacularly accurate asymptotic expansions and non-asymptotic scales. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 470 (2162), pp. 20130529, 16.

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External Links:

ISSN 1364-5021, Document, Link, MathReview (Eugenia N. Petropoulou), ZentralBlatt

Referenced by:

§10.22(v), §10.22(v).

Encodings:

BibTeX

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8: 10.22 Integrals

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§10.22(i) Indefinite Integrals

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Products

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Trigonometric Arguments

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Fractional Integral

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§10.22(v) Hankel Transform

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9: 15.14 Integrals

§15.14 Integrals

… ►Integrals of the form $\int x^{\alpha }{(x+t)}^{\beta }F(a,b;c;x)dx$ and more complicated forms are given in Apelblat (1983, pp. 370–387), Prudnikov et al. (1990, §§1.15 and 2.21), Gradshteyn and Ryzhik (2015, §7.5) and Koornwinder (2015). … ►Hankel transforms of hypergeometric functions are given in Oberhettinger (1972, §1.17) and Erdélyi et al. (1954b, §8.17). ►For other integral transforms see Erdélyi et al. (1954b), Prudnikov et al. (1992b, §4.3.43), and also §15.9(ii).

10: 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).

Encodings:

BibTeX

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