Further triangles of Seidel-Arnold type and continued fractions related to Euler and Springer numbers
type: Item
instance of: scholarly article
title: Further triangles of Seidel-Arnold type and continued fractions related to Euler and Springer numbers
zbMATH Open document ID: 0834.05004
published in: Advances in Applied Mathematics
publication date: 1996-03-31T00:00:00Z
review text: \textit{V. I. Arnold} [Russ. Math. Surv. 47, No. 1, 1-51 (1992; Zbl 0791.05001)] introduced two pairs of triangles of numbers that lead to simple algorithms for computing Springer numbers (arising from the expansion \(S(x)= {\text{cosh } x\over \text{cosh } 2x}+ {\text{sinh } x\over \text{cosh } 2x}\)) [\textit{T. A. Springer}, Nieuw Arch. Wiskd. III. Ser. 19, 30-36 (1971; Zbl 0224.05002)]. The author proved this approach on the base of Seidel type triangles [the author and \textit{G. Viennot}, Ann. Discrete Math. 6, 77-87 (1980; Zbl 0449.10011)], using only exponential generating functions. The method is carried over to ordinary generating functions, and their continued fraction expansions are given-- -in particular, for Euler, Springer, and Genocchi numbers. In addition, a new pair of triangles for Euler numbers is introduced, and the ``median'' Euler numbers are defined.
reviewed by: Indulis Strazdins
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 11B68
Mathematics Subject Classification ID: 11A55
Mathematics Subject Classification ID: 11B75
Mathematics Subject Classification ID: 11J70
zbMATH DE Number: 820049
zbMATH Keywords: Springer numbers
zbMATH Keywords: Seidel type triangles
zbMATH Keywords: generating functions
zbMATH Keywords: continued fraction
zbMATH Keywords: Genocchi numbers
zbMATH Keywords: Euler numbers
author: Dominique Dumont
MaRDI profile type: Publication
full work available at URL: aama.1995.1014
OpenAlex ID: W2029111462
DOI: 10.1006/AAMA.1995.1014
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description: scientific article; zbMATH DE number 820049