Code to Compute Asymptotic Contributions of Smooth Contributing Points

The code below computes asymptotic expansions of strictly or finitely minimal smooth contributing points, using Theorem 5.2 and Corollary 5.2 from the textbook. Note: The multivariate_generating_functions (mgf) package has the capability to perform similar computations, however for completeness (and because the mgf package currently needs work to fix various errors) we implement Theorem 5.2 directly using the DifferentialWeylAlgebra package.

Requirements: None

Example 5.1 (Asymptotics of Central Binomial Coefficients)

Example 5.2 (‘Asymptotics’ in an Irrational Direction)

Example 5.4 (Vanishing of Asymptotic Terms)

Example 5.5 (Asymptotics of a Multinomial Expansion)

Example 5.6 (Lattice Path Asymptotics)

Example 5.7 (Lonesum Matrices)

Example 5.9 (Asymptotics of Apéry Numbers)

Example 5.10 (Asymptotics of Bar Graphs)

Example 5.11 (Non-Finitely Minimal Critical Point)

Example 5.12 (Local Central Limit Theorem for Weighted Walks)