Intuitively, the biggest contribution to the contour integral is around the saddle point and estimating near the saddle-point gives us an estimate for the whole contour.
Flajolet, Philippe; Sedgewick, Robert (2009). Analytic Combinatorics(PDF). Cambridge University Press.
Hardy, G.H. (1949). Divergent Series (1st ed.). Oxford University Press.
Melczer, Stephen (2021). An Invitation to Analytic Combinatorics: From One to Several Variables(PDF). Springer Texts & Monographs in Symbolic Computation.
Pemantle, Robin; Wilson, Mark C. (2013). Analytic Combinatorics in Several Variables(PDF). Cambridge University Press.
Sedgewick, Robert. "4. Complex Analysis, Rational and Meromorphic Asymptotics" (PDF). Retrieved 4 November 2023.
Sedgewick, Robert. "8. Saddle-Point Asymptotics" (PDF). Retrieved 4 November 2023.
Szegő, Gabor (1975). Orthogonal Polynomials (4th ed.). American Mathematical Society.
Wilf, Herbert S. (2006). Generatingfunctionology(PDF) (3rd ed.). A K Peters, Ltd.
As of 4th November 2023, this article is derived in whole or in part from Wikibooks. The copyright holder has licensed the content in a manner that permits reuse under CC BY-SA 3.0 and GFDL. All relevant terms must be followed.
Further readingedit
Wikibooks has a book on the topic of: Analytic Combinatorics
De Bruijn, N.G. (1981). Asymptotic Methods in Analysis. Dover Publications.
Flajolet, Philippe; Odlyzko, Andrew (1990). "Singularity analysis of generating functions" (PDF). SIAM Journal on Discrete Mathematics. 1990 (3).
Mishna, Marni (2020). Analytic Combinatorics: A Multidimensional Approach. Taylor & Francis Group, LLC.