as%20Bessel%20polynomials
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11—18 of 18 matching pages
11: 6.20 Approximations
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Cody and Thacher (1968) provides minimax rational approximations for , with accuracies up to 20S.
Cody and Thacher (1969) provides minimax rational approximations for , with accuracies up to 20S.
MacLeod (1996b) provides rational approximations for the sine and cosine integrals and for the auxiliary functions and , with accuracies up to 20S.
Luke (1969b, pp. 41–42) gives Chebyshev expansions of , , and for , . The coefficients are given in terms of series of Bessel functions.
12: Bibliography I
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Computing zeros and orders of Bessel functions.
J. Comput. Appl. Math. 38 (1-3), pp. 169–184.
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The real roots of Bernoulli polynomials.
Ann. Univ. Turku. Ser. A I 37, pp. 1–20.
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Two families of orthogonal polynomials related to Jacobi polynomials.
Rocky Mountain J. Math. 21 (1), pp. 359–375.
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Bounds for the small real and purely imaginary zeros of Bessel and related functions.
Methods Appl. Anal. 2 (1), pp. 1–21.
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Classical and Quantum Orthogonal Polynomials in One Variable.
Encyclopedia of Mathematics and its Applications, Vol. 98, Cambridge University Press, Cambridge.
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13: Bibliography V
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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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Expansions in products of Heine-Stieltjes polynomials.
Constr. Approx. 15 (4), pp. 467–480.
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Error estimates for Rayleigh-Ritz approximations of eigenvalues and eigenfunctions of the Mathieu and spheroidal wave equation.
Constr. Approx. 20 (1), pp. 39–54.
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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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14: Software Index
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15: Bibliography
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Exact linearization of a Painlevé transcendent.
Phys. Rev. Lett. 38 (20), pp. 1103–1106.
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On the degrees of irreducible factors of higher order Bernoulli polynomials.
Acta Arith. 62 (4), pp. 329–342.
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Application of the combined nonlinear-condensation transformation to problems in statistical analysis and theoretical physics.
Comput. Phys. Comm. 150 (1), pp. 1–20.
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Computation of modified Bessel functions and their ratios.
Math. Comp. 28 (125), pp. 239–251.
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Repeated integrals and derivatives of
Bessel functions.
SIAM J. Math. Anal. 20 (1), pp. 169–175.
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16: 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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On the definition and properties of generalized - symbols.
J. Math. Phys. 20 (12), pp. 2398–2415.
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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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17: Bibliography W
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The Nahm equations, finite-gap potentials and Lamé functions.
J. Phys. A 20 (10), pp. 2679–2683.
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Tables of Summable Series and Integrals Involving Bessel Functions.
Holden-Day, San Francisco, CA.
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Algorithm 44: Bessel functions computed recursively.
Comm. ACM 4 (4), pp. 177–178.
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Asymptotic expansions of the generalized Bessel polynomials.
J. Comput. Appl. Math. 85 (1), pp. 87–112.
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The asymptotic expansion of the generalized Bessel function.
Proc. London Math. Soc. (2) 38, pp. 257–270.
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