Results 41 to 50 of about 1,536,850 (314)
Combinatorially interpreting generalized Stirling numbers [PDF]
, 2014 Let $w$ be a word in alphabet $\{x,D\}$ with $m$ $x$'s and $n$ $D$'s. Interpreting "$x$" as multiplication by $x$, and "$D$" as differentiation with respect to $x$, the identity $wf(x) = x^{m-n}\sum_k S_w(k) x^k D^k f(x)$, valid for any smooth function ...
Engbers, John +2 more
core +4 more sources
Generalized degenerate Bernoulli numbers and polynomials arising from Gauss hypergeometric function
Advances in Difference Equations, 2021 A new family of p-Bernoulli numbers and polynomials was introduced by Rahmani (J. Number Theory 157:350–366, 2015) with the help of the Gauss hypergeometric function.
Taekyun Kim +4 more
doaj +1 more source
A STUDY ON MULTI-STIRLING NUMBERS OF THE FIRST KIND
Fractals, 2022 In this paper, we define the multi-Stirling numbers of the first kind by means of the multiple logarithm and as a generalization of the Stirling numbers of the first kind.
Yuankui Ma +4 more
semanticscholar +1 more source
q-Differential equations for q-classical polynomials and q-Jacobi-Stirling numbers [PDF]
, 2015 We introduce, characterise and provide a combinatorial interpretation for the so-called q-Jacobi–Stirling numbers. This study is motivated by their key role in the (reciprocal) expansion of any power of a second order q-differential operator having the
Loureiro, Ana F., Zeng, J.
core +3 more sources
The Noncentral Version of the Whitney Numbers: A Comprehensive Study
International Journal of Mathematics and Mathematical Sciences, 2016 This paper is a comprehensive study of a certain generalization of Whitney-type and Stirling-type numbers which unifies the classical Whitney numbers, the translated Whitney numbers, the classical Stirling numbers, and the noncentral Stirling (or r ...
Mahid M. Mangontarum +2 more
doaj +1 more source
Some Identities of Degenerate Bell Polynomials
Mathematics, 2020 The new type degenerate of Bell polynomials and numbers were recently introduced, which are a degenerate version of Bell polynomials and numbers and are different from the previously introduced partially degenerate Bell polynomials and numbers.
Taekyun Kim +3 more
doaj +1 more source
Probabilistic Stirling Numbers of the Second Kind and Applications [PDF]
Journal of theoretical probability, 2020 Associated with each complex-valued random variable satisfying appropriate integrability conditions, we introduce a different generalization of the Stirling numbers of the second kind. Various equivalent definitions are provided.
J. Adell
semanticscholar +1 more source
Two closed forms for the Bernoulli polynomials [PDF]
, 2015 In the paper, the authors find two closed forms involving the Stirling numbers of the second kind and in terms of a determinant of combinatorial numbers for the Bernoulli polynomials and numbers.Comment: 7 ...
Chapman, Robin J., Qi, Feng
core +2 more sources
Problems for combinatorial numbers satisfying a class of triangular arrays
Lietuvos Matematikos Rinkinys, 2023 Numbers satisfying a class of triangular arrays, defined by a bivariate first-order linear difference equation with linear coefficients, include a wide range of combinatorial numbers: binomial coefficients, Morgan numbers, Stirling numbers of the first ...
Igoris Belovas
doaj +3 more sources
Normal ordering of degenerate integral powers of number operator and its applications
Applied Mathematics in Science and Engineering, 2022 The normal ordering of an integral power of the number operator in terms of boson operators is expressed with the help of the Stirling numbers of the second kind. As a ‘degenerate version’ of this, we consider the normal ordering of a degenerate integral
Taekyun Kim, Dae San Kim, Hye Kyung Kim
doaj +1 more source