.1994年世界杯小组分组_『网址:687.vii』2018世界杯直播咪咕_b5p6v3_2022年11月30日7时57分10秒_z9fzftt9n.cc
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11: 9.18 Tables
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Miller (1946) tabulates , for , for ; , for ; , for ; , , , (respectively , , , ) for . Precision is generally 8D; slightly less for some of the auxiliary functions. Extracts from these tables are included in Abramowitz and Stegun (1964, Chapter 10), together with some auxiliary functions for large arguments.
Zhang and Jin (1996, p. 338) tabulates and for to 8D or 8S.
National Bureau of Standards (1958) tabulates and for and ; for . Precision is 8D.
Gil et al. (2003c) tabulates the only positive zero of , the first 10 negative real zeros of and , and the first 10 complex zeros of , , , and . Precision is 11 or 12S.
§9.18(vii) Generalized Airy Functions
…12: 24.2 Definitions and Generating Functions
13: Errata
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References
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Version 1.0.21 (December 15, 2018)
… ►Version 1.0.20 (September 15, 2018)
… ►Version 1.0.19 (June 22, 2018)
… ►Version 1.0.18 (March 27, 2018)
…14: Bibliography E
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Angular Momentum in Quantum Mechanics.
3rd printing, with corrections, 2nd edition, Princeton University Press, Princeton, NJ.
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The numerical inversion of two classes of Kontorovich-Lebedev transform by direct quadrature.
J. Comput. Appl. Math. 61 (1), pp. 43–72.
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An upper bound for the zeros of the derivative of Bessel functions.
Rend. Circ. Mat. Palermo (2) 46 (1), pp. 123–130.
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A comparison of some methods for the evaluation of highly oscillatory integrals.
J. Comput. Appl. Math. 112 (1-2), pp. 55–69.
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The asymptotic behaviour of the inhomogeneous Airy function
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Math. Chronicle 12, pp. 99–104.
15: 8.21 Generalized Sine and Cosine Integrals
16: 18.30 Associated OP’s
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►where is given by (18.30.2) and (18.30.3), with , , and as in (18.9.2).
…where the generalized hypergeometric function is defined by (16.2.1).
►For corresponding corecursive associated Jacobi polynomials, corecursive associated polynomials being discussed in §18.30(vii), see Letessier (1995).
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and of (18.30.23) and (18.30.24) are, also, precisely those of (18.2.34) and (18.2.35), now expressed via the traditional, , , coefficients, rather than the monic, , , recursion coefficients.
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§18.30(vii) Corecursive and Associated Monic Orthogonal Polynomials
…17: Bibliography L
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The inhomogeneous Airy functions, and
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J. Chem. Phys. 72 (1), pp. 332–336.
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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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Two index laws for fractional integrals and derivatives.
J. Austral. Math. Soc. 14, pp. 385–410.
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Bessel transforms and rational extrapolation.
Numer. Math. 47 (1), pp. 1–14.
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Integrating some infinite oscillating tails.
J. Comput. Appl. Math. 12/13, pp. 109–117.
18: Bibliography O
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Studies on the Painlevé equations. I. Sixth Painlevé equation
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Ann. Mat. Pura Appl. (4) 146, pp. 337–381.
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A further method for the evaluation of zeros of Bessel functions and some new asymptotic expansions for zeros of functions of large order.
Proc. Cambridge Philos. Soc. 47, pp. 699–712.
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Some new asymptotic expansions for Bessel functions of large orders.
Proc. Cambridge Philos. Soc. 48 (3), pp. 414–427.
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Uniform asymptotic expansions for Weber parabolic cylinder functions of large orders.
J. Res. Nat. Bur. Standards Sect. B 63B, pp. 131–169.
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Iterative Solution of Nonlinear Equations in Several Variables.
Academic Press, New York.
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19: DLMF Project News
error generating summary20: Antony Ross Barnett
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► 2018) was Senior Research Fellow in the Mathematics Department, University of Waikato, Hamilton, New Zealand.
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