Laplace method for asymptotic expansions of integrals
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11—18 of 18 matching pages
11: Bibliography H
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Asymptotic expansion of Laplace transforms near the origin.
SIAM J. Math. Anal. 1 (1), pp. 118–130.
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Asymptotic expansion of a class of integral transforms with algebraically dominated kernels.
J. Math. Anal. Appl. 35 (2), pp. 405–433.
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Spherical Bessel expansions of sine, cosine, and exponential integrals.
Appl. Numer. Math. 34 (1), pp. 95–98.
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On the resurgence properties of the uniform asymptotic expansion of Bessel functions of large order.
Proc. Roy. Soc. London Ser. A 455, pp. 3917–3930.
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Asymptotic expansions of Mathieu functions in wave mechanics.
J. Comput. Phys. 21 (3), pp. 319–325.
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12: Bibliography K
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An indirect method for evaluating certain infinite integrals.
Z. Angew. Math. Phys. 29 (3), pp. 380–386.
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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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The method of isomonodromic deformations and the asymptotics of the solutions of the “complete” third Painlevé equation.
Mat. Sb. (N.S.) 134(176) (3), pp. 421–444, 448 (Russian).
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Two new asymptotic methods in the theory of wave propagation in inhomogeneous media.
Sov. Phys. Acoust. 14, pp. 1–17.
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A Handbook of Methods of Approximate Fourier Transformation and Inversion of the Laplace Transformation.
Mir, Moscow.
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13: 2.10 Sums and Sequences
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§2.10(iii) Asymptotic Expansions of Entire Functions
►The asymptotic behavior of entire functions defined by Maclaurin series can be approached by converting the sum into a contour integral by use of the residue theorem and applying the methods of §§2.4 and 2.5. … ►By application of Laplace’s method (§2.3(iii)) and use again of (5.11.7), we obtain … ►§2.10(iv) Taylor and Laurent Coefficients: Darboux’s Method
… ►See also Flajolet and Odlyzko (1990).14: Bibliography L
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A note on the uniform asymptotic expansion of integrals with coalescing endpoint and saddle points.
J. Phys. A 19 (3), pp. 329–335.
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Error bounds for asymptotic expansions of Laplace convolutions.
SIAM J. Math. Anal. 25 (6), pp. 1537–1553.
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Uniform asymptotic expansions of symmetric elliptic integrals.
Constr. Approx. 17 (4), pp. 535–559.
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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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Asymptotic expansions of symmetric standard elliptic integrals.
SIAM J. Math. Anal. 31 (4), pp. 754–775.
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15: 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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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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A further method for the evaluation of zeros of Bessel functions and some new asymptotic expansions for zeros of functions of large order.
Proc. Cambridge Philos. Soc. 47, pp. 699–712.
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Uniform, exponentially improved, asymptotic expansions for the generalized exponential integral.
SIAM J. Math. Anal. 22 (5), pp. 1460–1474.
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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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16: Bibliography W
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Asymptotic expansions for second-order linear difference equations with a turning point.
Numer. Math. 94 (1), pp. 147–194.
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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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17: Bibliography G
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On high precision methods for computing integrals involving Bessel functions.
Math. Comp. 33 (147), pp. 1049–1057.
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On the generalization of a method for computing Bessel function integrals.
J. Comput. Appl. Math. 6 (2), pp. 167–168.
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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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A method for evaluating certain Bessel integrals.
Z. Angew. Math. Phys. 30 (4), pp. 722–723.
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Asymptotische Entwicklungen für unvollständige Gammafunktionen.
Forum Math. 3 (2), pp. 105–141 (German).
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18: Bibliography D
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Asymptotic Methods in Analysis.
2nd edition, Bibliotheca Mathematica, Vol. IV, North-Holland Publishing Co., Amsterdam.
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Asymptotic Expansions: Their Derivation and Interpretation.
Academic Press, London-New York.
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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 approximation of Mathieu functions.
Methods Appl. Anal. 1 (2), pp. 143–168.
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Error analysis in a uniform asymptotic expansion for the generalised exponential integral.
J. Comput. Appl. Math. 80 (1), pp. 127–161.
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