Asymptotics of multivariate sequences I. Smooth points of the singular variety

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:97

Article

Pemantle, R ; Wilson, MC

关键词: generating function;    recurrence;    linear difference equation;    contour methods;    central limit;    oscillating integral;    Cauchy integral formula;   

DOI  :  10.1006/jcta.2001.3201

来源: Elsevier

【 摘 要 】

Given a multivariate generating function F(z(1), ..., z(d)) = Sigma a(r1, ..., rd) z(1)(r1) (...) z(d)(rd), we determine asymptotics for the coefficients. Our approach is to use Cauchy's integral formula near singular points of F, resulting in a tractable oscillating integral. This paper treats the case where the singular point of F is a smooth point of a surface of poles. Companion papers treat singular points of F where the local geometry is more complicated, and for which other methods of analysis are not known. (C) 2001 Elsevier Science.

【 授权许可】

Free