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A probabilistic generalization of the Bell polynomials
Motivated by an interconnection between the probabilistic Stirling numbers of the second kind and the Bell polynomials studied by Adell and Lekuona...
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Degenerate poly-Bell polynomials and numbers
Numerous mathematicians have studied ‘poly’ as one of the generalizations to special polynomials, such as Bernoulli, Euler, Cauchy, and Genocchi...
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State polynomials: positivity, optimization and nonlinear Bell inequalities
This paper introduces state polynomials, i.e., polynomials in noncommuting variables and formal states of their products. A state analog of Artin’s...
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Generalizations of Stirling-like and Bell-like Numbers
Stirling and Bell numbers play a fundamental role in enumerative combinatorics, they count, among others, partitions of a finite set. We give a...
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Bell based Apostol-Bernoulli polynomials and its properties
In this present paper, we define a generating function of mix type polynomials known as Bell based Apostol-Bernoulli polynomials of order
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Poly-central factorial sequences and poly-central-Bell polynomials
In this paper, we introduce poly-central factorial sequences and poly-central Bell polynomials arising from the polyexponential functions, reducing...
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Nonlinear Inverse Relations of the Bell Polynomials via the Lagrange Inversion Formula (II)
In this paper, by means of the classical Lagrange inversion formula, the authors establish a general nonlinear inverse relation as the solution to...
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Integrability and Exact Solutions of the (2+1)-dimensional KdV Equation with Bell Polynomials Approach
In this paper, the bilinear formalism, bilinear Bäcklund transformations and Lax pair of the (2+1)-dimensional KdV equation are constructed by the...
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Recurrences and Congruences for Higher-Order Geometric Polynomials and Related Numbers
We obtain new recurrence relations, an explicit formula, and convolution identities for higher-order geometric polynomials. These relations...
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Some properties of degenerate complete and partial Bell polynomials
In this paper, we study degenerate complete and partial Bell polynomials and establish some new identities for those polynomials. In addition, we...
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Some new formulas of complete and incomplete degenerate Bell polynomials
The aim of this paper is to study the complete and incomplete degenerate Bell polynomials, which are degenerate versions of the complete and...
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Mean-Value Theorem for Multiple Trigonometric Sums on the Sequence of Bell Polynomials
AbstractA mean-value theorem for multiple trigonometric (exponential) sums on the sequence of Bell polynomials is proved. It generalizes I. M....
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Fubini Numbers and Polynomials of Graphs
In this paper, we introduce the Fubini number and Fubini polynomial of a graph in connection with the enumeration of ordered independent partitions...
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Some identities of Lah–Bell polynomials
Recently, the n th Lah–Bell number was defined as the number of ways a set of n elements can be partitioned into nonempty linearly ordered subsets for...
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A Probabilistic Extension of the Fubini Polynomials
In this paper, we present a probabilistic extension of the Fubini polynomials and numbers associated with a random variable satisfying some...
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Degenerate Bell polynomials associated with umbral calculus
Carlitz initiated a study of degenerate Bernoulli and Euler numbers and polynomials which is the pioneering work on degenerate versions of special...
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Analysis of Generating Functions for Special Words and Numbers and Algorithms for Computation
Our aim is to construct and compute efficient generating functions enumerating the k -ary Lyndon words having prime number length which arise in many...
