• Eulerian number asymptotics

Result: Eulerian number asymptotics

Title:
Eulerian number asymptotics
Authors:
Eldar Giladi, Joseph B. Keller
Source:
Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences. 445:291-303
Publisher Information:
The Royal Society, 1994.
Publication Year:
1994
Subject Terms:
Perturbations, asymptotics of solutions to ordinary differential equations, Asymptotic approximations, asymptotic expansions (steepest descent, etc.), Eulerian number, ray method, asymptotic, 0101 mathematics, Bernoulli and Euler numbers and polynomials, Asymptotic enumeration, 01 natural sciences
Document Type:
Academic journal Article
File Description:
application/xml
Language:
English
ISSN:
2053-9177
0962-8444
DOI:
10.1098/rspa.1994.0062
Access URL:
https://zbmath.org/646921
https://doi.org/10.1098/rspa.1994.0062
https://www.jstor.org/stable/52599
https://ui.adsabs.harvard.edu/abs/1994RSPSA.445..291G/abstract
Rights:
Royal Society Data Sharing and Accessibility
Accession Number:
edsair.doi.dedup.....5f03d18521cab62d0317c12c784525ff
Database:
OpenAIRE

Further Information

Asymptotic formulae for the eulerian numbers A(n, k) for n ≫ 1 are obtained directly from their recursion relation by the ray method and the method of matched asymptotic expansions. These are formal methods, so they do not prove that the formulae are asymptotic, although they suggest it. The formulae agree with the previously known results where those results are valid. They also agree very well with the exact values of A(n, k) for 1 ≼ n ≼ 170, and the agreement improves as n increases.