application%20to%20asymptotic%20expansions
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1—10 of 16 matching pages
1: Bibliography D
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Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory.
Comm. Pure Appl. Math. 52 (11), pp. 1335–1425.
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Convergent Liouville-Green expansions for second-order linear differential equations, with an application to Bessel functions.
Proc. Roy. Soc. London Ser. A 440, pp. 37–54.
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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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Convergent expansions for solutions of linear ordinary differential equations having a simple turning point, with an application to Bessel functions.
Stud. Appl. Math. 107 (3), pp. 293–323.
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Convergent expansions for solutions of linear ordinary differential equations having a simple pole, with an application to associated Legendre functions.
Stud. Appl. Math. 113 (3), pp. 245–270.
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2: Bibliography N
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On an asymptotic expansion of the Kontorovich-Lebedev transform.
Applicable Anal. 39 (4), pp. 249–263.
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On an asymptotic expansion of the Kontorovich-Lebedev transform.
Methods Appl. Anal. 3 (1), pp. 98–108.
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Error bounds for the asymptotic expansion of the Hurwitz zeta function.
Proc. A. 473 (2203), pp. 20170363, 16.
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Uniform asymptotic expansion for the incomplete beta function.
SIGMA Symmetry Integrability Geom. Methods Appl. 12, pp. 101, 5 pages.
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Error bounds and exponential improvement for Hermite’s asymptotic expansion for the gamma function.
Appl. Anal. Discrete Math. 7 (1), pp. 161–179.
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3: 2.11 Remainder Terms; Stokes Phenomenon
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►For second-order differential equations, see Olde Daalhuis and Olver (1995a), Olde Daalhuis (1995, 1996), and Murphy and Wood (1997).
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►The transformations in §3.9 for summing slowly convergent series can also be very effective when applied to divergent asymptotic series.
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►shows that this direct estimate is correct to almost 3D.
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►For example, extrapolated values may converge to an accurate value on one side of a Stokes line (§2.11(iv)), and converge to a quite inaccurate value on the other.
4: Bibliography S
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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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Uniform asymptotic expansions of modified Mathieu functions.
J. Reine Angew. Math. 247, pp. 1–17.
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Asymptotic expansions of Mellin transforms and analogues of Watson’s lemma.
SIAM J. Math. Anal. 16 (4), pp. 896–906.
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A simple approach to asymptotic expansions for Fourier integrals of singular functions.
Appl. Math. Comput. 216 (11), pp. 3378–3385.
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Uniform asymptotic expansions of Hermite polynomials.
M. Phil. thesis, City University of Hong Kong.
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5: Bibliography W
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Asymptotic expansions of some matrix argument hypergeometric functions, with applications to macromolecules.
Ann. Inst. Statist. Math. 45 (3), pp. 467–475.
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On uniform asymptotic expansion of definite integrals.
J. Approximation Theory 7 (1), pp. 76–86.
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Asymptotic expansions of the Kontorovich-Lebedev transform.
Appl. Anal. 12 (3), pp. 161–172.
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Applications of some recent results in asymptotic expansions.
Congr. Numer. 37, pp. 145–182.
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The asymptotic expansion of the generalized Bessel function.
Proc. London Math. Soc. (2) 38, pp. 257–270.
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6: Bibliography M
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Asymptotic expansions for the zeros of certain special functions.
J. Comput. Appl. Math. 145 (2), pp. 261–267.
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Explicit error terms for asymptotic expansions of Stieltjes transforms.
J. Inst. Math. Appl. 22 (2), pp. 129–145.
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Exact remainders for asymptotic expansions of fractional integrals.
J. Inst. Math. Appl. 24 (2), pp. 139–147.
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Asymptotic expansion of a multiple integral.
SIAM J. Math. Anal. 18 (6), pp. 1630–1637.
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On asymptotic expansions of ellipsoidal wave functions.
Math. Nachr. 32, pp. 157–172.
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7: Bibliography F
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On the reversion of an asymptotic expansion and the zeros of the Airy functions.
SIAM Rev. 41 (4), pp. 762–773.
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Asymptotic expansions of a class of hypergeometric polynomials with respect to the order. II.
J. Math. Anal. Appl. 7 (3), pp. 440–451.
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Asymptotic expansions of a class of hypergeometric polynomials with respect to the order.
J. Math. Anal. Appl. 6 (3), pp. 394–403.
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Asymptotic expansions of a class of hypergeometric polynomials with respect to the order. III.
J. Math. Anal. Appl. 12 (3), pp. 593–601.
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On the asymptotic expansion of Mellin transforms.
SIAM J. Math. Anal. 18 (1), pp. 273–282.
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8: Bibliography C
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Asymptotic expansion of the first elliptic integral.
SIAM J. Math. Anal. 16 (5), pp. 1072–1092.
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Asymptotic estimates for generalized Stirling numbers.
Analysis (Munich) 20 (1), pp. 1–13.
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Uniform asymptotic expansion of an integral with a saddle point, a pole and a branch point.
Proc. Roy. Soc. London Ser. A 426, pp. 273–286.
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On the asymptotic expansion of Airy’s integral.
Proc. Glasgow Math. Assoc. 6, pp. 113–115.
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Asymptotic Expansions.
Cambridge Tracts in Mathematics and Mathematical Physics, Cambridge University Press, New York.
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9: Bibliography V
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Airy Functions and Applications to Physics.
Second edition, Imperial College Press, London.
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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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Generalized Associated Legendre Functions and their Applications.
World Scientific Publishing Co. Inc., Singapore.
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A note on the asymptotic expansion of generalized hypergeometric functions.
Anal. Appl. (Singap.) 12 (1), pp. 107–115.
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Asymptotic expansion of the generalized hypergeometric function as for
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Anal. Appl. (Singap.) 21 (2), pp. 535–545.
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10: Bibliography L
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An asymptotic estimate for the Bernoulli and Euler numbers.
Canad. Math. Bull. 20 (1), pp. 109–111.
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Uniform asymptotic expansions of symmetric elliptic integrals.
Constr. Approx. 17 (4), pp. 535–559.
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A systematic “saddle point near a pole” asymptotic method with application to the Gauss hypergeometric function.
Stud. Appl. Math. 127 (1), pp. 24–37.
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Asymptotic expansions of the Whittaker functions for large order parameter.
Methods Appl. Anal. 6 (2), pp. 249–256.
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Adjusted forms of the Fourier coefficient asymptotic expansion and applications in numerical quadrature.
Math. Comp. 25 (113), pp. 87–104.
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