modified spherical Bessel functions
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21—30 of 34 matching pages
21: Bibliography S
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A code to evaluate modified Bessel functions based on the continued fraction method.
Comput. Phys. Comm. 105 (2-3), pp. 263–272.
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Bounds for ratios of modified Bessel functions and associated Turán-type inequalities.
J. Math. Anal. Appl. 374 (2), pp. 516–528.
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Numerical evaluation of spherical Bessel transforms via fast Fourier transforms.
J. Comput. Phys. 100 (2), pp. 294–296.
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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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On the calculation of complex zeros of the modified Bessel function of the second kind.
Dokl. Akad. Nauk SSSR 280 (2), pp. 296–299.
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22: 18.15 Asymptotic Approximations
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►where is the Bessel function (§10.2(ii)), and
…The latter expansions are in terms of Bessel functions, and are uniform in complex -domains not containing neighborhoods of 1.
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►These expansions are in terms of Bessel functions and modified Bessel functions, respectively.
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In Terms of Bessel Functions
… ►Here denotes the Bessel function (§10.2(ii)), denotes its envelope (§2.8(iv)), and is again an arbitrary small positive constant. …23: Bibliography Z
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On the Computation of Zeros of Bessel and Bessel-related Functions.
In Proceedings of the Sixth International Colloquium on
Differential Equations (Plovdiv, Bulgaria, 1995), D. Bainov (Ed.),
Utrecht, pp. 409–416.
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A note on the -method approximations for the Bessel functions
and
.
Comput. Math. Appl. 31 (9), pp. 63–70.
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Chebyshev series approximations for the Bessel function
of complex argument.
Appl. Math. Comput. 88 (2-3), pp. 275–286.
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Tables and formulae for the spherical functions
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Translated by E. L. Albasiny, Pergamon Press, Oxford.
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Tablitsy modifitsirovannykh funktsii Besselya s mnimym indeksom
.
Vyčisl. Centr Akad. Nauk SSSR, Moscow.
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24: 33.9 Expansions in Series of Bessel Functions
§33.9 Expansions in Series of Bessel Functions
►§33.9(i) Spherical Bessel Functions
… ►where the function is as in §10.47(ii), , , and … ►§33.9(ii) Bessel Functions and Modified Bessel Functions
►In this subsection the functions , , and are as in §§10.2(ii) and 10.25(ii). …25: 14.15 Uniform Asymptotic Approximations
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►Here and are the modified Bessel functions (§10.25(ii)).
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►For the Bessel functions
and see §10.2(ii), and for the
functions associated with and see §2.8(iv).
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►See also Olver (1997b, pp. 311–313) and §18.15(iii) for a generalized asymptotic expansion in terms of elementary functions for Legendre polynomials as with fixed.
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►(The inverse hyperbolic functions again take their principal values.)
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26: Bibliography B
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Algorithms for evaluating spherical Bessel functions in the complex domain.
Zh. Vychisl. Mat. i Mat. Fiz. 28 (12), pp. 1779–1788, 1918.
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Asymptotic expansions of the modified Bessel function of the third kind of imaginary order.
SIAM J. Appl. Math. 15, pp. 1315–1323.
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The Calculation of Spherical Bessel Functions and Coulomb Functions.
In Computational Atomic Physics: Electron and Positron Collisions
with Atoms and Ions, K. Bartschat and J. Hinze (Eds.),
pp. 181–202.
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Associated Legendre polynomials, ordinary and modified spherical harmonics.
Comput. Phys. Comm. 5 (5), pp. 390–394.
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Algorithm 484: Evaluation of the modified Bessel functions K0(Z) and K1(Z) for complex arguments.
Comm. ACM 17 (9), pp. 524–526.
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27: Bibliography M
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Chebyshev expansions for modified Struve and related functions.
Math. Comp. 60 (202), pp. 735–747.
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Spherical Harmonics. An Elementary Treatise on Harmonic Functions with Applications.
3rd edition, International Series of Monographs in Pure and Applied Mathematics, Vol. 98, Pergamon Press, Oxford.
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On the evaluation of the integral over the product of two spherical Bessel functions.
J. Math. Phys. 32 (3), pp. 642–648.
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Calculation of the modified Bessel functions of the second kind with complex argument.
Math. Comp. 20 (95), pp. 407–412.
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Analytic expressions for integrals of products of spherical Bessel functions.
J. Phys. A 24 (7), pp. 1435–1453.
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28: 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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Bessel functions of matrix argument.
Ann. of Math. (2) 61 (3), pp. 474–523.
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Bessel function expansions of Coulomb wave functions.
J. Math. Phys. 26 (4), pp. 656–659.
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29: Bibliography T
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LSFBTR: A subroutine for calculating spherical Bessel transforms.
Comput. Phys. Comm. 30 (1), pp. 93–99.
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On the numerical evaluation of the modified Bessel function of the third kind.
J. Comput. Phys. 19 (3), pp. 324–337.
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Steepest descent paths for integrals defining the modified Bessel functions of imaginary order.
Methods Appl. Anal. 1 (1), pp. 14–24.
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The numerical computation of special functions by use of quadrature rules for saddle point integrals. II. Gamma functions, modified Bessel functions and parabolic cylinder functions.
Report TW 183/78
Mathematisch Centrum, Amsterdam, Afdeling Toegepaste
Wiskunde.
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Further comments on the computation of modified Bessel function ratios.
Math. Comp. 35 (151), pp. 937–939.
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30: Bibliography V
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Accurate calculation of the modified Mathieu functions of integer order.
Quart. Appl. Math. 65 (1), pp. 1–23.
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Integrating products of Bessel functions with an additional exponential or rational factor.
Comput. Phys. Comm. 178 (8), pp. 578–590.
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Some novel infinite series of spherical Bessel functions.
Quart. Appl. Math. 42 (3), pp. 321–324.
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On the localization and computation of zeros of Bessel functions.
Z. Angew. Math. Mech. 77 (6), pp. 467–475.
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The topological degree theory for the localization and computation of complex zeros of Bessel functions.
Numer. Funct. Anal. Optim. 18 (1-2), pp. 227–234.