Laplace's method on a computer algebra system with an application to the real valued modified Bessel functions

DOI10.1016/S0377-0427(02)00364-3zbMath1013.65015MaRDI QIDQ1860383

Bruce R. Fabijonas

Publication date: 23 February 2003

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

algorithmmodified Bessel functionsasymptotic expansionsPuiseux seriesLaplace's methodLaplace-type integralspower series reversion

Mathematics Subject Classification ID

Computation of special functions and constants, construction of tables (65D20) Laplace transform (44A10) Numerical methods for integral transforms (65R10) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10)

Related Items (1)

On the coefficients that arise from Laplace's method

Uses Software

• gfun
• Maple

Cites Work

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• Power-series unification and reversion
• Symbolic asymptotics: Multiseries of inverse functions
• Fast computation of some asymptotic functional inverses
• Numerical algorithms for uniform Airy-type asymptotic expansions
• Evaluation of the modified Bessel function of the third kind of imaginary orders
• Steepest descent paths for integrals defining the modified Bessel functions of imaginary order
• Formal solution of nonlinear simultaneous equations: Reversion of series in several variables
• Computing the Generating Function of a Series Given Its First Few Terms
• Tabulation of Coefficients for Operations on Taylor Series
• Reversion of a formal power series
• Bessel Functions of Purely Imaginary Order, with an Application to Second-Order Linear Differential Equations Having a Large Parameter
• Solutions to a Problem in Power Series Reversion
• Fast Algorithms for Manipulating Formal Power Series
• Reversion of power series and the extended Raney coefficients
• GFUN
• On the Reversion of an Asymptotic Expansion and the Zeros of the Airy Functions
• A note on extension of the lagrange inversion formula
• Functional Composition Patterns and Power Series Reversion
• Solution of transcendental equations by series reversion
• Asymptotic Expansions of the Modified Bessel Function of the Third Kind of Imaginary Order
• ON THE CHOICE OF STANDARD SOLUTIONS FOR A HOMOGENEOUS LINEAR DIFFERENTIAL EQUATION OF THE SECOND ORDER

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