for%20Bessel%20and%20Hankel%20functions
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1: 10.75 Tables
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The main tables in Abramowitz and Stegun (1964, Chapter 9) give to 15D, , , , to 10D, to 8D, ; , , , 8D; , , , , 5D or 5S; , , , , 10S; modulus and phase functions , , , , 8D.
§10.75(iii) Zeros and Associated Values of the Bessel Functions, Hankel Functions, and their Derivatives
… ►Abramowitz and Stegun (1964, Chapter 9) tabulates , , , , , , 5D (10D for ), , , , , , , 5D (8D for ), , , , 5D. Also included are the first 5 zeros of the functions , , , , for various values of and in the interval , 4–8D.
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.
2: 10.3 Graphics
§10.3 Graphics
►§10.3(i) Real Order and Variable
►For the modulus and phase functions , , , and see §10.18. … ►§10.3(ii) Real Order, Complex Variable
… ►§10.3(iii) Imaginary Order, Real Variable
…3: 10.73 Physical Applications
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§10.73(i) Bessel and Modified Bessel Functions
… ► … ► … ► … ►The functions , , , and arise in the solution (again by separation of variables) of the Helmholtz equation in spherical coordinates (§1.5(ii)): …4: Bibliography
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Regular and irregular Coulomb wave functions expressed in terms of Bessel-Clifford functions.
J. Math. Physics 33, pp. 111–116.
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Integrals involving Bickley and Bessel functions in radiative transfer, and generalized exponential integral functions.
J. Heat Transfer 118 (3), pp. 789–792.
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Computation of modified Bessel functions and their ratios.
Math. Comp. 28 (125), pp. 239–251.
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A subroutine package for Bessel functions of a complex argument and nonnegative order.
Technical Report
Technical Report SAND85-1018, Sandia National Laboratories, Albuquerque, NM.
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Repeated integrals and derivatives of
Bessel functions.
SIAM J. Math. Anal. 20 (1), pp. 169–175.
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5: 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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Integrals of three Bessel functions and Legendre functions. I.
J. Math. Phys. 26 (4), pp. 633–644.
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Integrals of three Bessel functions and Legendre functions. II.
J. Math. Phys. 26 (4), pp. 645–655.
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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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Bessel functions and representation theory. I.
J. Functional Analysis 22 (2), pp. 73–105.
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6: Bibliography B
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A program for computing the Riemann zeta function for complex argument.
Comput. Phys. Comm. 20 (3), pp. 441–445.
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Coulomb functions (negative energies).
Comput. Phys. Comm. 20 (3), pp. 447–458.
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A short table of the functions
, from to
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Phil. Mag. Series 7 20, pp. 343–347.
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Bessel functions and modular relations of higher type and hyperbolic differential equations.
Comm. Sém. Math. Univ. Lund [Medd. Lunds Univ. Mat. Sem.] 1952 (Tome Supplementaire), pp. 12–20.
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Introduction to Bessel Functions.
Dover Publications Inc., New York.
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7: Bibliography S
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Transformations of the Jacobian amplitude function and its calculation via the arithmetic-geometric mean.
SIAM J. Math. Anal. 20 (6), pp. 1514–1528.
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Numerical evaluation of the Hankel transform.
Comput. Phys. Comm. 116 (2-3), pp. 278–294.
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Uniform asymptotic forms of modified Mathieu functions.
Quart. J. Mech. Appl. Math. 20 (3), pp. 365–380.
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A Maple package for symmetric functions.
J. Symbolic Comput. 20 (5-6), pp. 755–768.
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Numerical Methods Based on Sinc and Analytic Functions.
Springer Series in Computational Mathematics, Vol. 20, Springer-Verlag, New York.
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8: Bibliography K
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The computation of the sums of negative even powers of roots of Bessel functions.
Doklady Akad. Nauk SSSR (N.S.) 77, pp. 561–564.
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Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library.
ACM Trans. Math. Software 20 (4), pp. 447–459.
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Calculation of the complex zeros of Hankel functions and their derivatives.
Zh. Vychisl. Mat. i Mat. Fiz. 25 (11), pp. 1628–1643, 1741.
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Methods of computing the Riemann zeta-function and some generalizations of it.
USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.
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Bessel Functions and their Applications.
Analytical Methods and Special Functions, Vol. 8, Taylor & Francis Ltd., London-New York.
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9: Bibliography R
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A code to calculate (high order) Bessel functions based on the continued fractions method.
Comput. Phys. Comm. 76 (3), pp. 381–388.
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Applied Bessel Functions.
Dover Publications Inc., New York.
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Computation of Hankel (Bessel) functions of complex index and argument by numerical integration of a Schläfli contour integral.
Ž. Vyčisl. Mat. i Mat. Fiz. 13, pp. 1415–1424, 1636.
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Partial fractions expansions and identities for products of Bessel functions.
J. Math. Phys. 46 (4), pp. 043509–1–043509–18.
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Finite-sum rules for Macdonald’s functions and Hankel’s symbols.
Integral Transform. Spec. Funct. 10 (2), pp. 115–124.
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10: 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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