Asymptotic Methods for Integrals
From MaRDI portal
Publication:3191273
DOI10.1142/9195zbMath1312.41002OpenAlexW590791627MaRDI QIDQ3191273
Publication date: 1 October 2014
Published in: Series in Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1142/9195
Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Research exposition (monographs, survey articles) pertaining to approximations and expansions (41-02) Computational aspects of special functions (33F99)
Related Items
Large \(z\) asymptotics for special function solutions of Painlevé II in the complex plane ⋮ Quantum carpets in leaky boxes ⋮ On new formulas for the cumulative distribution function of the noncentral chi-square distribution ⋮ A convergent version of Watson's lemma for double integrals ⋮ Exact expansions of Hankel transforms and related integrals ⋮ Uniform asymptotic expansions for Laguerre polynomials and related confluent hypergeometric functions ⋮ Large deviations for high-dimensional random projections of \(\ell_p^n\)-balls ⋮ Uniform asymptotic expansion for the incomplete beta function ⋮ An analytic representation of the second symmetric standard elliptic integral in terms of elementary functions ⋮ Special function solutions of Painlevé equations: theory, asymptotics and applications ⋮ Asymptotic computation of classical orthogonal polynomials ⋮ Error bounds for the large-argument asymptotic expansions of the Hankel and Bessel functions ⋮ A new asymptotic representation and inversion method for the Student's t distribution ⋮ A generalized modified Bessel function and a higher level analogue of the theta transformation formula ⋮ An asymptotic formula for the number of \(n\)-dimensional representations of \(\mathrm{SU}(3)\) ⋮ New asymptotic representations of the noncentral t‐distribution ⋮ The rate of convergence of a generalization of Post-Widder operators and Rathore operators ⋮ Entropic uncertainty measures for large dimensional hydrogenic systems ⋮ New series expansions for the ℋ-function of communication theory ⋮ Computation of parabolic cylinder functions having complex argument ⋮ Quantum curl forces ⋮ Bound-constrained global optimization of functions with low effective dimensionality using multiple random embeddings ⋮ Multiple sampling and interpolation in Bergman spaces ⋮ Escaping superoscillations ⋮ Mathematical analysis for stochastic model of Alzheimer's disease ⋮ Asymptotics of Genocchi polynomials and higher order Genocchi polynomials using residues ⋮ Page curves for general interacting systems ⋮ Noniterative Computation of Gauss--Jacobi Quadrature ⋮ Asymptotic expansions of Jacobi polynomials and of the nodes and weights of Gauss-Jacobi quadrature for large degree and parameters in terms of elementary functions ⋮ Asymptotic expansion of the integral with two oscillations on an infinite interval ⋮ The length of self-avoiding walks on the complete graph ⋮ Uniform approximations of the first symmetric elliptic integral in terms of elementary functions ⋮ Simplifying large spin bootstrap in Mellin space ⋮ Numerical methods for the computation of the confluent and Gauss hypergeometric functions ⋮ On a vectorized version of a generalized Richardson extrapolation process ⋮ Asymptotic analysis of the Wright function with a large parameter ⋮ Improving Beckner's bound via Hermite functions ⋮ Unnamed Item ⋮ On the computation and inversion of the cumulative noncentral beta distribution function ⋮ High-precision computation of the confluent hypergeometric functions via Franklin-Friedman expansion ⋮ Numerical evaluation of Airy-type integrals arising in uniform asymptotic analysis ⋮ Cardy limits of 6d superconformal theories ⋮ An extension of Laplace's method ⋮ Asymptotic correlations in gapped and critical topological phases of 1D quantum systems ⋮ Asymptotics for the twisted eta-product and applications to sign changes in partitions ⋮ Asymptotic expansions of Kummer hypergeometric functions with three asymptotic parameters \(a\), \(b\) and \(z\) ⋮ Large-deviation theory for a Brownian particle on a ring: a WKB approach ⋮ Uniform asymptotic expansions for solutions of the parabolic cylinder and Weber equations ⋮ Asymptotic expansions for Wiener–Hopf equations ⋮ A convergent and asymptotic Laplace method for integrals ⋮ Integrals whose saddle-point expansions terminate ⋮ Entropic functionals of Laguerre and Gegenbauer polynomials with large parameters ⋮ Asymptotic expansions of Kummer hypergeometric functions for large values of the parameters ⋮ A distribution function from population genetics statistics using Stirling numbers of the first kind: Asymptotics, inversion and numerical evaluation