asymptotic%20approximations%20for%20coefficients
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11—19 of 19 matching pages
11: 12.11 Zeros
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§12.11(ii) Asymptotic Expansions of Large Zeros
… ►§12.11(iii) Asymptotic Expansions for Large Parameter
►For large negative values of the real zeros of , , , and can be approximated by reversion of the Airy-type asymptotic expansions of §§12.10(vii) and 12.10(viii). …The first two coefficients are given by … ►where the numerical coefficients have been rounded off. …12: Bibliography D
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On the high-order coefficients in the uniform asymptotic expansion for the incomplete gamma function.
Methods Appl. Anal. 5 (3), pp. 223–247.
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Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions.
SIAM J. Math. Anal. 20 (3), pp. 744–760.
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Uniform asymptotic approximation of Mathieu functions.
Methods Appl. Anal. 1 (2), pp. 143–168.
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Asymptotic approximations for the Jacobi and ultraspherical polynomials, and related functions.
Methods Appl. Anal. 6 (3), pp. 21–56.
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Uniform asymptotic approximations for incomplete Riemann zeta functions.
J. Comput. Appl. Math. 190 (1-2), pp. 339–353.
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13: Bibliography S
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Calculator function approximation.
Amer. Math. Monthly 90 (5), pp. 317–325.
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Semiclassical approximations to - and -coefficients for quantum-mechanical coupling of angular momenta.
J. Mathematical Phys. 16 (10), pp. 1971–1988.
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The accuracy of iterated JWBK approximations for Coulomb radial functions.
Comput. Phys. Comm. 32 (2), pp. 115–119.
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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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Approximate Calculation of Multiple Integrals.
Prentice-Hall Inc., Englewood Cliffs, N.J..
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14: Bibliography V
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On the coefficients of the modular invariant
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Nederl. Akad. Wetensch. Proc. Ser. A. 56 = Indagationes
Math. 15 56, pp. 389–400.
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Rational approximations for exponential integrals
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Acad. Roy. Belg. Bull. Cl. Sci. (5) 56, pp. 1064–1072.
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Symbolic evaluation of coefficients in Airy-type asymptotic expansions.
J. Math. Anal. Appl. 269 (1), pp. 317–331.
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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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Approximation of eigenvalues of some differential equations by zeros of orthogonal polynomials.
J. Comput. Appl. Math. 213 (2), pp. 488–500.
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15: Bibliography N
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On an integral transform involving a class of Mathieu functions.
SIAM J. Math. Anal. 20 (6), pp. 1500–1513.
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Reduction and evaluation of elliptic integrals.
Math. Comp. 20 (94), pp. 223–231.
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Uniform Asymptotic Approximations of Solutions of Second-order Linear Differential Equations, with a Coalescing Simple Turning Point and Simple Pole.
Ph.D. Thesis, University of Maryland, College Park, MD.
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Approximations for the Bessel and Struve functions.
Math. Comp. 43 (168), pp. 551–556.
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A table of integrals of the error functions.
J. Res. Nat. Bur. Standards Sect B. 73B, pp. 1–20.
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16: Bibliography K
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Asymptotic approximations for the first incomplete elliptic integral near logarithmic singularity.
J. Comput. Appl. Math. 205 (1), pp. 186–206.
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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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Uniform asymptotic approximations for the Meixner-Sobolev polynomials.
Anal. Appl. (Singap.) 10 (3), pp. 345–361.
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Exponentially accurate uniform asymptotic approximations for integrals and Bleistein’s method revisited.
Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 469 (2153), pp. 20130008, 12.
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Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation. I.
Inverse Problems 20 (4), pp. 1165–1206.
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17: 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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18: Bibliography R
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Rational Chebyshev approximation by Remes’ algorithms.
Numer. Math. 7 (4), pp. 322–330.
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On the definition and properties of generalized - symbols.
J. Math. Phys. 20 (12), pp. 2398–2415.
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Remark on Algorithm 498: Airy functions using Chebyshev series approximations.
ACM Trans. Math. Software 7 (3), pp. 404–405.
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Uniform asymptotic approximations to the solutions of the Orr-Sommerfeld equation. I. Plane Couette flow.
Studies in Appl. Math. 53, pp. 91–110.
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Uniform asymptotic approximations to the solutions of the Orr-Sommerfeld equation. II. The general theory.
Studies in Appl. Math. 53, pp. 217–224.
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19: 18.40 Methods of Computation
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