uniform expansions
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11—20 of 76 matching pages
11: Bibliography O
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On the resurgence properties of the uniform asymptotic expansion of the incomplete gamma function.
Methods Appl. Anal. 5 (4), pp. 425–438.
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Uniform asymptotic expansions for hypergeometric functions with large parameters. I.
Analysis and Applications (Singapore) 1 (1), pp. 111–120.
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Uniform asymptotic expansions for hypergeometric functions with large parameters. II.
Analysis and Applications (Singapore) 1 (1), pp. 121–128.
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Uniform asymptotic expansions for hypergeometric functions with large parameters. III.
Analysis and Applications (Singapore) 8 (2), pp. 199–210.
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Scattering by a parabolic cylinder—a uniform asymptotic expansion.
J. Math. Phys. 26 (4), pp. 854–860.
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12: Bibliography D
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Uniform asymptotic expansions for prolate spheroidal functions with large parameters.
SIAM J. Math. Anal. 17 (6), pp. 1495–1524.
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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 expansions for oblate spheroidal functions I: Positive separation parameter
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Proc. Roy. Soc. Edinburgh Sect. A 121 (3-4), pp. 303–320.
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Uniform asymptotic expansions for Charlier polynomials.
J. Approx. Theory 112 (1), pp. 93–133.
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Uniform asymptotic expansions for associated Legendre functions of large order.
Proc. Roy. Soc. Edinburgh Sect. A 133 (4), pp. 807–827.
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13: 10.72 Mathematical Applications
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►Bessel functions and modified Bessel functions are often used as approximants in the construction of uniform asymptotic approximations and expansions for solutions of linear second-order differential equations containing a parameter.
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►These expansions are uniform with respect to , including the turning point and its neighborhood, and the region of validity often includes cut neighborhoods (§1.10(vi)) of other singularities of the differential equation, especially irregular singularities.
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►If has a double zero , or more generally is a zero of order , , then uniform asymptotic approximations (but not expansions) can be constructed in terms of Bessel functions, or modified Bessel functions, of order .
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►These asymptotic expansions are uniform with respect to , including cut neighborhoods of , and again the region of uniformity often includes cut neighborhoods of other singularities of the differential equation.
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14: 2.1 Definitions and Elementary Properties
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§2.1(iv) Uniform Asymptotic Expansions
… ►As in §2.1(iv), generalized asymptotic expansions can also have uniformity properties with respect to parameters. …15: Bibliography F
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Uniform asymptotic expansions for hypergeometric functions with large parameters IV.
Anal. Appl. (Singap.) 12 (6), pp. 667–710.
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Uniform asymptotic expansions of certain classes of Meijer -functions for a large parameter.
SIAM J. Math. Anal. 4 (3), pp. 482–507.
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Uniform asymptotic expansions of a class of Meijer -functions for a large parameter.
SIAM J. Math. Anal. 14 (6), pp. 1204–1253.
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A uniform asymptotic expansion of the Jacobi polynomials with error bounds.
Canad. J. Math. 37 (5), pp. 979–1007.
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Uniform asymptotic expansions of Laguerre polynomials.
SIAM J. Math. Anal. 19 (5), pp. 1232–1248.
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16: Bibliography T
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Uniform asymptotic expansions of confluent hypergeometric functions.
J. Inst. Math. Appl. 22 (2), pp. 215–223.
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Laplace type integrals: Transformation to standard form and uniform asymptotic expansions.
Quart. Appl. Math. 43 (1), pp. 103–123.
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Uniform asymptotic expansions of a class of integrals in terms of modified Bessel functions, with application to confluent hypergeometric functions.
SIAM J. Math. Anal. 21 (1), pp. 241–261.
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Uniform asymptotic expansions of integrals: A selection of problems.
J. Comput. Appl. Math. 65 (1-3), pp. 395–417.
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Numerical algorithms for uniform Airy-type asymptotic expansions.
Numer. Algorithms 15 (2), pp. 207–225.
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17: 12.14 The Function
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§12.14(ix) Uniform Asymptotic Expansions for Large Parameter
… ►Airy-type uniform asymptotic expansions can be used to include either one of the turning points . … ►Positive ,
… ►Airy-type Uniform Expansions
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§12.10 Uniform Asymptotic Expansions for Large Parameter
… ►§12.10(vi) Modifications of Expansions in Elementary Functions
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… ►19: 10.20 Uniform Asymptotic Expansions for Large Order
§10.20 Uniform Asymptotic Expansions for Large Order
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10.20.5
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10.20.9
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►For asymptotic properties of the expansions (10.20.4)–(10.20.6) with respect to large values of see §10.41(v).
20: Bibliography W
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Uniform asymptotic expansion of via a difference equation.
Numer. Math. 91 (1), pp. 147–193.
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Estimates for the error term in a uniform asymptotic expansion of the Jacobi polynomials.
Anal. Appl. (Singap.) 1 (2), pp. 213–241.
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Uniform asymptotic expansion of the Jacobi polynomials in a complex domain.
Proc. Roy. Soc. London Ser. A 460, pp. 2569–2586.
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On uniform asymptotic expansion of definite integrals.
J. Approximation Theory 7 (1), pp. 76–86.
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