large%20parameters
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1—10 of 17 matching pages
1: Bibliography D
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Complex zeros of cylinder functions.
Math. Comp. 20 (94), pp. 215–222.
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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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Bessel functions of purely imaginary order, with an application to second-order linear differential equations having a large parameter.
SIAM J. Math. Anal. 21 (4), pp. 995–1018.
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Conical functions with one or both parameters large.
Proc. Roy. Soc. Edinburgh Sect. A 119 (3-4), pp. 311–327.
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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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2: Bibliography N
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Reduction and evaluation of elliptic integrals.
Math. Comp. 20 (94), pp. 223–231.
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The resurgence properties of the large order asymptotics of the Anger-Weber function I.
J. Class. Anal. 4 (1), pp. 1–39.
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The resurgence properties of the large order asymptotics of the Anger-Weber function II.
J. Class. Anal. 4 (2), pp. 121–147.
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On the large argument asymptotics of the Lommel function via Stieltjes transforms.
Asymptot. Anal. 91 (3-4), pp. 265–281.
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Coulomb Functions for Large Values of the Parameter
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Technical report
Atomic Energy of Canada Limited, Chalk
River, Ontario.
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3: 28.16 Asymptotic Expansions for Large
4: 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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Sur certaines sommes des intégral-cosinus.
Bull. Soc. Math. Phys. Serbie 12, pp. 13–20 (French).
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The third Appell function for one large variable.
J. Approx. Theory 165, pp. 60–69.
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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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5: Bibliography O
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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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Legendre functions with both parameters large.
Philos. Trans. Roy. Soc. London Ser. A 278, pp. 175–185.
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Whittaker functions with both parameters large: Uniform approximations in terms of parabolic cylinder functions.
Proc. Roy. Soc. Edinburgh Sect. A 86 (3-4), pp. 213–234.
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6: 28.8 Asymptotic Expansions for Large
§28.8 Asymptotic Expansions for Large
… ►Barrett’s Expansions
… ►The approximations apply when the parameters and are real and large, and are uniform with respect to various regions in the -plane. … ►Dunster’s Approximations
… ►7: 3.8 Nonlinear Equations
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►for all sufficiently large, where and are independent of , then the sequence is said to have convergence of the
th order.
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►Then the sensitivity of a simple zero to changes in is given by
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►For moderate or large values of it is not uncommon for the magnitude of the right-hand side of (3.8.14) to be very large compared with unity, signifying that the computation of zeros of polynomials is often an ill-posed problem.
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►Consider and .
We have and .
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8: 12.10 Uniform Asymptotic Expansions for Large Parameter
§12.10 Uniform Asymptotic Expansions for Large Parameter
… ►§12.10(vi) Modifications of Expansions in Elementary Functions
… ► … ►Modified Expansions
… ►9: 30.9 Asymptotic Approximations and Expansions
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