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Probabilistic central Bell polynomials

R. Xu, Y. Ma, T. Kim, D. S. Kim, S. Boulaars

Abstract

Let Y be a random variable whose moment generating function exists in a neighborhood of the origin. In this paper, we study the probabilistic central Bell polynomials associated with random variable Y, as probabilistic extension of the central Bell polynomials. In addition, we investigate the probabilistic central factorial numbers of the second kind associated with Y and the probabilistic central Fubini polynomials associated with Y. The aim of this paper is to derive some properties, explicit expressions, certain identities and recurrence relations for those polynomials and numbers.

Probabilistic central Bell polynomials

Abstract

Let Y be a random variable whose moment generating function exists in a neighborhood of the origin. In this paper, we study the probabilistic central Bell polynomials associated with random variable Y, as probabilistic extension of the central Bell polynomials. In addition, we investigate the probabilistic central factorial numbers of the second kind associated with Y and the probabilistic central Fubini polynomials associated with Y. The aim of this paper is to derive some properties, explicit expressions, certain identities and recurrence relations for those polynomials and numbers.
Paper Structure (3 sections, 15 theorems, 63 equations)

This paper contains 3 sections, 15 theorems, 63 equations.

Table of Contents

  1. Introduction
  2. Probabilistic Central Bell polynomials
  3. Conclusion

Key Result

Theorem 2.1

For $n\ge k\ge 0$, we have

Theorems & Definitions (15)

  • Theorem 2.1
  • Theorem 2.2
  • Theorem 2.3
  • Theorem 2.4
  • Theorem 2.5
  • Theorem 2.6
  • Theorem 2.7
  • Theorem 2.8
  • Theorem 2.9: Convolution formula
  • Theorem 2.10
  • ...and 5 more