Book contents
- Frontmatter
- Dedication
- Contents
- Preface to the second edition
- Preface to the first edition
- List of Symbols
- Part I Combinatorial Enumeration
- Part II Mathematical Background
- 4 Fourier–Laplace integrals in one variable
- 5 Multivariate Fourier–Laplace integrals
- 6 Laurent series, amoebas, and convex geometry
- Part III Multivariate Enumeration
- Appendix A Integration on manifolds
- Appendix B Algebraic topology
- Appendix C Residue forms and classical Morse theory
- Appendix D Stratification and stratified Morse theory
- References
- Author Index
- Subject Index
4 - Fourier–Laplace integrals in one variable
from Part II - Mathematical Background
Published online by Cambridge University Press: 08 February 2024
Book contents
- Frontmatter
- Dedication
- Contents
- Preface to the second edition
- Preface to the first edition
- List of Symbols
- Part I Combinatorial Enumeration
- Part II Mathematical Background
- 4 Fourier–Laplace integrals in one variable
- 5 Multivariate Fourier–Laplace integrals
- 6 Laurent series, amoebas, and convex geometry
- Part III Multivariate Enumeration
- Appendix A Integration on manifolds
- Appendix B Algebraic topology
- Appendix C Residue forms and classical Morse theory
- Appendix D Stratification and stratified Morse theory
- References
- Author Index
- Subject Index
Summary
This chapter develops methods to compute asymptotics of univariate Fourier–Laplace integrals (which combine exponential decay and oscillation) and saddle point approximations. We illustrate both analytic and smooth methods for asymptotics.
- Type
- Chapter
- Information
- Analytic Combinatorics in Several Variables , pp. 89 - 113Publisher: Cambridge University PressPrint publication year: 2024