Asymptotic Analysis of Dotsenko–Fateev Integrals

Asymptotic Expansions for Integrals

Asymptotic Analysis of Finite Di erences and Rice Integrals

summary by Philippe Dumas and Dani ele Gardy] Rice's method is designed to estimate sums Df n = n X k=0 (?1) k n k ! f k ; (1) where the sequence f n can be extended as an analytic function (n). The asymptotics of the sequence f n are assumed to be known, and the problem is to obtain the asymptotic behaviour of the sequence Df n. The obvious bound jDf n j 2 n max k jf k j is often disappointing...

Asymptotic approximation of exponential integrals

1 Preliminaries 1 1.1 What this is . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Problem statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.3 Big-O and small-o notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.4 Definition: Asymptotic approximation ...

Asymptotic Approximation of Marginal Likelihood Integrals

We study the asymptotics of marginal likelihood integrals for discrete models using resolution of singularities from algebraic geometry, a method introduced recently by Sumio Watanabe. We briefly describe the statistical and mathematical foundations of this method, and explore how Newton diagrams and toric modifications help solve the problem. The approximations are then compared with exact com...

Asymptotic Expansions of Symmetric Standard Elliptic Integrals

Symmetric standard elliptic integrals are considered when one of their parameters is larger than the others. Distributional approach is used for deriving five convergent expansions of these integrals in inverse powers of the respective five possible asymptotic parameters. Four of these expansions involve also a logarithmic term in the asymptotic variable. Coefficients of these expansions are ob...