Shanks' convergence acceleration transform, Padé approximants and partitions

George E. Andrews, Ian P. Goulden, David M. Jackson

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

Shanks developed a method for accelerating the convergence of sequences. When applied to classical sequences in number theory, Shanks' transform yields some famous identities of Euler and Gauss. It is shown here that the Padé approximants for the little q-Jacobi polynomials can be used to explain and extend Shanks' observations. The combinatorial significance of these results is also discussed.

Original languageEnglish (US)
Pages (from-to)70-84
Number of pages15
JournalJournal of Combinatorial Theory, Series A
Volume43
Issue number1
DOIs
StatePublished - Sep 1986

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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