integrals of Bessel and Hankel functions
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11: 10.75 Tables
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§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.
§10.75(iv) Integrals of Bessel Functions
… ►§10.75(v) Modified Bessel Functions and their Derivatives
… ►§10.75(vii) Integrals of Modified Bessel Functions
…12: 10.41 Asymptotic Expansions for Large Order
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§10.41(v) Double Asymptotic Properties (Continued)
… ►We first prove that for the expansions (10.20.6) for the Hankel functions and the -asymptotic property applies when , respectively. …We then extend the validity of this property from to in the sector in the case of , and to in the sector in the case of . … ►13: 13.10 Integrals
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§13.10(i) Indefinite Integrals
… ►§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). ►§13.10(vi) Other Integrals
…14: Bibliography C
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Determination of -zeros of Hankel functions.
Comput. Phys. Comm. 32 (3), pp. 333–339.
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Incomplete Hankel and modified Bessel functions: A class of special functions for electromagnetics.
IEEE Trans. Antennas and Propagation 52 (12), pp. 3373–3389.
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Numerical techniques for finding -zeros of Hankel functions.
Math. Comp. 24 (110), pp. 413–422.
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The zeros of Hankel functions as functions of their order.
Numer. Math. 7 (3), pp. 238–250.
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Zeros of the Hankel function of real order out of the principal Riemann sheet.
J. Comput. Appl. Math. 37 (1-3), pp. 89–99.
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15: 13.4 Integral Representations
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13.4.2
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16: 13.23 Integrals
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§13.23(i) Laplace and Mellin Transforms
… ►§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). … ►§13.23(v) Other Integrals
…17: 10.21 Zeros
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§10.21(ix) Complex Zeros
… ►The zeros of have a similar pattern to those of . … ► … ►§10.21(xiv) -Zeros
►For information on zeros of Bessel and Hankel functions as functions of the order, see Cochran (1965), Cochran and Hoffspiegel (1970), Hethcote (1970), Conde and Kalla (1979), and Sandström and Ackrén (2007).18: 10.54 Integral Representations
§10.54 Integral Representations
… ►19: Bibliography H
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Expansions for the probability function in series of Čebyšev polynomials and Bessel functions.
Bul. Akad. Štiince RSS Moldoven. 1976 (1), pp. 77–80, 96 (Russian).
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Spherical Bessel expansions of sine, cosine, and exponential integrals.
Appl. Numer. Math. 34 (1), pp. 95–98.
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Tables of the Modified Hankel Functions of Order One-Third and of their Derivatives.
Harvard University Press, Cambridge, MA.
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Error bounds for asymptotic approximations of zeros of Hankel functions occurring in diffraction problems.
J. Mathematical Phys. 11 (8), pp. 2501–2504.
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Bessel function expansions of Coulomb wave functions.
J. Math. Phys. 26 (4), pp. 656–659.
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20: Bibliography L
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Numerical evaluation of integrals containing a spherical Bessel function by product integration.
J. Math. Phys. 22 (7), pp. 1399–1413.
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Evaluation of Bessel function integrals with algebraic singularities.
J. Comput. Appl. Math. 37 (1-3), pp. 101–112.
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A note on the computation of integrals involving products of trigonometric and Bessel functions.
Math. Comp. 27 (124), pp. 871–872.
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Integral representation of the Hankel function in terms of parabolic cylinder functions.
Quart. J. Mech. Appl. Math. 23 (3), pp. 315–327.
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Integrals of Bessel Functions.
McGraw-Hill Book Co., Inc., New York.
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