On a Convolution of Eulerian Numbers: 10609

1999 ◽  
Vol 106 (7) ◽  
pp. 690
Author(s):  
Donald E. Knuth ◽  
David Callan
Keyword(s):  
Eulerian Numbers

scholarly journals Automated Proofs for Some Stirling Number Identities

10.37236/726 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
Manuel Kauers ◽  
Carsten Schneider
Keyword(s):  
Stirling Number ◽  
Eulerian Numbers ◽  
Difference Fields

We present computer-generated proofs for some summation identities for ($q$-)Stirling and ($q$-)Eulerian numbers that were obtained by combining a recent summation algorithm for Stirling number identities with a recurrence solver for difference fields.

scholarly journals New Eulerian Numbers of Type $D$

10.37236/5514 ◽  
2016 ◽  
Vol 23 (1) ◽  
Author(s):  
Anna Borowiec ◽  
Wojciech Młotkowski
Keyword(s):  
Recurrence Relation ◽  
Generating Function ◽  
Probability Distributions ◽  
Type A ◽  
Eulerian Numbers ◽  
Eulerian Polynomials ◽  
Type D

We introduce a new array of type $D$ Eulerian numbers, different from that studied by Brenti, Chow and Hyatt. We find in particular the recurrence relation, Worpitzky formula and the generating function. We also find the probability distributions whose moments are Eulerian polynomials of type $A$, $B$ and $D$.

Beyond the Euler summation formula

2004 ◽  
Vol 88 (513) ◽  
pp. 432-440 ◽  
Author(s):  
Barry Lewis
Keyword(s):  
Summation Formula ◽  
Eulerian Numbers ◽  
The Subject ◽  
Established Technique

The Eulerian numbers are not strangers to readers of the Gazette but they are not normally associated with the subject of this article, despite the similarity of their names. This article seeks to use Eulerian numbers in generalised telescoping sums, a role that is a powerful extension of an established technique – the Euler summation formula.

scholarly journals On Fully Degenerate Daehee Numbers and Polynomials of the Second Kind

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Sang Jo Yun ◽  
Jin-Woo Park
Keyword(s):  
Exponential Function ◽  
Special Functions ◽  
Eulerian Numbers

In a study, Carlitz introduced the degenerate exponential function and applied that function to Bernoulli and Eulerian numbers and degenerate special functions have been studied by many researchers. In this paper, we define the fully degenerate Daehee polynomials of the second kind which are different from other degenerate Daehee polynomials and derive some new and interesting identities and properties of those polynomials.

Postorder trees and Eulerian numbers

1991 ◽  
Vol 28 (7) ◽  
pp. 703-712
Author(s):  
Thomas P. Whaley
Keyword(s):  
Eulerian Numbers

Eulerian number asymptotics

1994 ◽  
Vol 445 (1924) ◽  
pp. 291-303 ◽  
Keyword(s):  
Formal Methods ◽  
Asymptotic Expansions ◽  
Recursion Relation ◽  
Matched Asymptotic Expansions ◽  
Ray Method ◽  
Eulerian Numbers ◽  
Eulerian Number ◽  
Asymptotic Formulae

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.

Sign in / Sign up

Export Citation Format

Share Document