Asymptotics of Some Convolutional Recurrences

Edward A. Bender, Adri B. Olde Daalhuis, Zhicheng Gao, L. Bruce Richmond, Nicholas Wormald

Research output: Contribution to journalArticlepeer-review

Abstract

We study the asymptotic behavior of the terms in sequences satisfying recurrences of the form a(n)=a(n-1) + Sigma(n-d)(k=d) f(n, k)a(k)a(n-k) where, very roughly speaking, f(n, k) behaves like a product of reciprocals of binomial coefficients. Some examples of such sequences from map enumerations, Airy constants, and Painleve I equations are discussed in detail.

Original languageEnglish
Article numberR1
Pages (from-to)-
Number of pages11
JournalElectronic Journal of Combinatorics
Volume17
Issue number1
Publication statusPublished - 5 Jan 2010

Keywords

  • 1ST PAINLEVE EQUATION
  • RICCATI EQUATION
  • NONLINEAR ODES
  • WIENER INDEX
  • TREES
  • HYPERASYMPTOTICS
  • SINGULARITY

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