asymptotic%20approximations
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21—26 of 26 matching pages
21: 25.12 Polylogarithms
22: Bibliography I
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The real roots of Bernoulli polynomials.
Ann. Univ. Turku. Ser. A I 37, pp. 1–20.
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Centre for Experimental and Constructive Mathematics, Simon Fraser University, Canada.
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Asymptotics of the Askey-Wilson and -Jacobi polynomials.
SIAM J. Math. Anal. 17 (6), pp. 1475–1482.
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On the asymptotic analysis of the Painlevé equations via the isomonodromy method.
Nonlinearity 7 (5), pp. 1291–1325.
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23: Bibliography O
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On the asymptotics for late coefficients in uniform asymptotic expansions of integrals with coalescing saddles.
Methods Appl. Anal. 7 (4), pp. 727–745.
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An error analysis of the modified Clenshaw method for evaluating Chebyshev and Fourier series.
J. Inst. Math. Appl. 20 (3), pp. 379–391.
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Error bounds for stationary phase approximations.
SIAM J. Math. Anal. 5 (1), pp. 19–29.
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Asymptotic approximations and error bounds.
SIAM Rev. 22 (2), pp. 188–203.
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Asymptotic expansions of the coefficients in asymptotic series solutions of linear differential equations.
Methods Appl. Anal. 1 (1), pp. 1–13.
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24: Bibliography P
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Automatic computation of Bessel function integrals.
Comput. Phys. Comm. 25 (3), pp. 289–295.
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Chebyshev series approximations for the zeros of the Bessel functions.
J. Comput. Phys. 53 (1), pp. 188–192.
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Approximation for the turning points of Bessel functions.
J. Comput. Phys. 64 (1), pp. 253–257.
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On the maximum errors of polynomial approximations defined by interpolation and by least squares criteria.
Comput. J. 9 (4), pp. 404–407.
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Algorithm 498: Airy functions using Chebyshev series approximations.
ACM Trans. Math. Software 1 (4), pp. 372–379.
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25: 18.40 Methods of Computation
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►These quadrature weights and abscissas will then allow construction of a convergent sequence of approximations to , as will be considered in the following paragraphs.
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Stieltjes Inversion via (approximate) Analytic Continuation
… ►Results of low ( to decimal digits) precision for are easily obtained for to . … ►Equation (18.40.7) provides step-histogram approximations to , as shown in Figure 18.40.1 for and , shown here for the repulsive Coulomb–Pollaczek OP’s of Figure 18.39.2, with the parameters as listed therein. … ►In Figure 18.40.2 the approximations were carried out with a precision of 50 decimal digits.26: Bibliography G
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Exactification of the Poincaré asymptotic expansion of the Hankel integral: spectacularly accurate asymptotic expansions and non-asymptotic scales.
Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 470 (2162), pp. 20130529, 16.
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Algorithm 726: ORTHPOL — a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules.
ACM Trans. Math. Software 20 (1), pp. 21–62.
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Gauss quadrature approximations to hypergeometric and confluent hypergeometric functions.
J. Comput. Appl. Math. 139 (1), pp. 173–187.
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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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Mutual integrability, quadratic algebras, and dynamical symmetry.
Ann. Phys. 217 (1), pp. 1–20.
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