scholarly journals On fully degenerate Bell numbers and polynomials

Filomat ◽  
2020 ◽  
Vol 34 (2) ◽  
pp. 507-514
Author(s):  
Dmitry Dolgy ◽  
Dae Kim ◽  
Taekyun Kim ◽  
Jongkyum Kwon
Keyword(s):  
Bell Numbers ◽  
Degenerate Version

Recently, the partially degenerate Bell numbers and polynomials were introduced as a degenerate version of Bell numbers and polynomials. In this paper, as a further degeneration of them, we study fully degenerate Bell numbers and polynomials. Among other things, we derive various expressions for the fully degenerate Bell numbers and polynomials.

scholarly journals Complete and incomplete Bell polynomials associated with Lah–Bell numbers and polynomials

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Taekyun Kim ◽  
Dae San Kim ◽  
Lee-Chae Jang ◽  
Hyunseok Lee ◽  
Han-Young Kim
Keyword(s):  
Bell Polynomials ◽  
Bell Numbers ◽  
Bell Number ◽  
Finite Sums

AbstractThe nth r-extended Lah–Bell number is defined as the number of ways a set with $n+r$ n + r elements can be partitioned into ordered blocks such that r distinguished elements have to be in distinct ordered blocks. The aim of this paper is to introduce incomplete r-extended Lah–Bell polynomials and complete r-extended Lah–Bell polynomials respectively as multivariate versions of r-Lah numbers and the r-extended Lah–Bell numbers and to investigate some properties and identities for these polynomials. From these investigations we obtain some expressions for the r-Lah numbers and the r-extended Lah–Bell numbers as finite sums.

Bell numbers, determinants and series

2013 ◽  
Vol 123 (2) ◽  
pp. 151-166 ◽  
Author(s):  
P K SAIKIA ◽  
DEEPAK SUBEDI
Keyword(s):  
Bell Numbers

Some inequalities for the Bell numbers

2017 ◽  
Vol 127 (4) ◽  
pp. 551-564 ◽  
Author(s):  
Feng Qi
Keyword(s):  
Bell Numbers

Stirling and Bell Numbers

2020 ◽  
pp. 277-300
Author(s):  
Craig P. Bauer
Keyword(s):  
Bell Numbers

Complementary Bell Numbers: Arithmetical Properties and Wilf’s Conjecture

2013 ◽  
pp. 23-56
Author(s):  
Tewodros Amdeberhan ◽  
Valerio De Angelis ◽  
Victor H. Moll
Keyword(s):  
Bell Numbers ◽  
Wilf’S Conjecture

Bell–Sheffer exponential polynomials of the second kind

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Pierpaolo Natalini ◽  
Paolo Emilio Ricci
Keyword(s):  
Higher Order ◽  
Bell Numbers ◽  
Integer Sequences ◽  
Exponential Polynomials ◽  
Sheffer Polynomials

AbstractIn recent papers, new sets of Sheffer and Brenke polynomials based on higher order Bell numbers and several integer sequences related to them have been studied. In the present paper, new sets of Bell–Sheffer polynomials are introduced. Connections with Bell numbers are shown.

scholarly journals A Note on Some Identities of New Type Degenerate Bell Polynomials

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1086 ◽  
Author(s):  
Taekyun Kim ◽  
Dae San Kim ◽  
Hyunseok Lee ◽  
Jongkyum Kwon
Keyword(s):  
Stirling Numbers ◽  
Bell Polynomials ◽  
New Type ◽  
Degenerate Version

Recently, the partially degenerate Bell polynomials and numbers, which are a degenerate version of Bell polynomials and numbers, were introduced. In this paper, we consider the new type degenerate Bell polynomials and numbers, and obtain several expressions and identities on those polynomials and numbers. In more detail, we obtain an expression involving the Stirling numbers of the second kind and the generalized falling factorial sequences, Dobinski type formulas, an expression connected with the Stirling numbers of the first and second kinds, and an expression involving the Stirling polynomials of the second kind.

Bell Numbers and Variant Sequences Derived from a General Functional Differential Equation

Integers ◽  
2009 ◽  
Vol 9 (5) ◽  
Author(s):  
H. W. Gould ◽  
Jocelyn Quaintance
Keyword(s):  
Differential Equation ◽  
Functional Differential Equation ◽  
Bell Numbers ◽  
Functional Differential

AbstractIt is well known that the Bell numbers

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