Hankel%20loop%20integral
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11: 10.3 Graphics
12: 10.75 Tables
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Achenbach (1986) tabulates , , , , , 20D or 18–20S.
§10.75(iii) Zeros and Associated Values of the Bessel Functions, Hankel Functions, and their Derivatives
… ►Döring (1966) tabulates all zeros of , , , , that lie in the sector , , to 10D. Some of the smaller zeros of and for are also included.
Kerimov and Skorokhodov (1985b) tabulates 50 zeros of the principal branches of and , 8D.
Bickley et al. (1952) tabulates or , or , , (.01 or .1) 10(.1) 20, 8S; , , , or , 10S.
13: 20 Theta Functions
Chapter 20 Theta Functions
…14: Bibliography G
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A new application of the discrete Laguerre polynomials in the numerical evaluation of the Hankel transform of a strongly decreasing even function.
J. Comput. Phys. 42 (2), pp. 277–287.
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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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Algorithm 726: ORTHPOL — a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules.
ACM Trans. Math. Software 20 (1), pp. 21–62.
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Algorithm 939: computation of the Marcum Q-function.
ACM Trans. Math. Softw. 40 (3), pp. 20:1–20:21.
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Mutual integrability, quadratic algebras, and dynamical symmetry.
Ann. Phys. 217 (1), pp. 1–20.
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15: Bibliography C
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Generalized hypergeometric functions and the evaluation of scalar one-loop integrals in Feynman diagrams.
J. Comput. Appl. Math. 115 (1-2), pp. 93–99.
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Determination of -zeros of Hankel functions.
Comput. Phys. Comm. 32 (3), pp. 333–339.
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A quadrature formula for the Hankel transform.
Numer. Algorithms 9 (2), pp. 343–354.
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Optimized fast Hankel transform filters.
Geophysical Prospecting 38 (5), pp. 545–568.
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Computation of Hankel transforms.
SIAM Rev. 14 (2), pp. 278–285.
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16: 10.76 Approximations
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§10.76(ii) Bessel Functions, Hankel Functions, and Modified Bessel Functions
… ►Real Variable and Order Integrals
…17: 10.4 Connection Formulas
18: 10.73 Physical Applications
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►See Krivoshlykov (1994, Chapter 2, §2.2.10; Chapter 5, §5.2.2), Kapany and Burke (1972, Chapters 4–6; Chapter 7, §A.1), and Slater (1942, Chapter 4, §§20, 25).
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►The functions , , , and arise in the solution (again by separation of variables) of the Helmholtz equation in spherical coordinates (§1.5(ii)):
…With the spherical harmonic defined as in §14.30(i), the solutions are of the form with , , , or , depending on the boundary conditions.
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19: 10.9 Integral Representations
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