Globally Exact Asymptotics for Integrals with Arbitrary Order Saddles

DOI10.1137/17M1154217zbMath1408.41023arXiv1710.10073OpenAlexW3100475825MaRDI QIDQ4637260

No author found.

Publication date: 18 April 2018

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1710.10073

zbMATH Keywords

error boundsasymptotic expansionssaddle pointshyperasymptoticsintegral asymptotics

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Remainders in approximation formulas (41A80) Critical points of functions and mappings on manifolds (58K05)

Related Items (7)

Error bounds for the asymptotic expansions of the Hermite polynomials ⋮ Nanoptera and Stokes curves in the 2-periodic Fermi-Pasta-Ulam-Tsingou equation ⋮ Standing lattice solitons in the discrete NLS equation with saturation ⋮ Three-dimensional capillary waves due to a submerged source with small surface tension ⋮ Proofs of Two Conjectures on the Real Zeros of the Cylinder and Airy Functions ⋮ Dingle’s final main rule, Berry’s transition, and Howls’ conjecture ^* ⋮ Logarithmic catastrophes and Stokes’s phenomenon in waves at horizons

Uses Software

• DLMF

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An explicit formula for the coefficients in Laplace's method
• Toward Picard-Lefschetz theory of path integrals, complex saddles and resurgence
• The devil's invention: Asymptotic, superasymptotic and hyperasymptotic series
• Hyperasymptotic solutions of second-order ordinary differential equations with a singularity of arbitrary integer rank
• Hyperterminants. II
• Oscillatory integrals and phenomena beyond all algebraic orders with applications to homoclinic orbits in reversible systems
• On the asymptotics for late coefficients in uniform asymptotic expansions of integrals with coalescing saddles
• Deconstructing zero: resurgence, supersymmetry and complex saddles
• Asymptotische Entwicklungen von Besselschen und Hankelschen Funktionen für große Werte des Arguments und der Ordnung
• Global asymptotics for multiple integrals with boundaries.
• Hyperasymptotic solutions of second-order linear differential equations. I
• Exponentially small expansions of the Wright function on the Stokes lines
• Error bounds for the large-argument asymptotic expansions of the Hankel and Bessel functions
• The Exponentially Convergent Trapezoidal Rule
• Complexified Path Integrals, Exact Saddles, and Supersymmetry
• The Resurgence Properties of the Incomplete Gamma Function II
• Hyperasymptotics for integrals with saddles
• Hyperasymptotics for integrals with finite endpoints
• Hyperasymptotic solutions of higher order linear differential equations with a singularity of rank one
• Unfolding the high orders of asymptotic expansions with coalescing saddles: singularity theory, crossover and duality
• Error bounds for the method of steepest descents
• Overlapping Stokes smoothings: survival of the error function and canonical catastrophe integrals
• Exponentially improved asymptotic solutions of ordinary differential equations. II. Irregular singularities of rank one
• Hyperasymptotics for multidimensional integrals, exact remainder terms and the global connection problem
• Uniform asymptotic smoothing of Stokes’s discontinuities
• Numerical Methods for Special Functions

This page was built for publication: Globally Exact Asymptotics for Integrals with Arbitrary Order Saddles