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Probabilistic bivariate Bell polynomials

Taekyun Kim, Dae san Kim

Abstract

Let Y be a random variable whose moment generating function exists in some neighborhood of the origin. We consider the probabilistic bivariate Bell polynomials associated with Y and the probabilistic bivariate r-Bell polynomials associated with Y. For those polynomials, we derive the recurrence relations corresponding to the ones found by Zheng and Li for the bivariate Bell polynomials and the bivariate r-Bell polynomials.

Probabilistic bivariate Bell polynomials

Abstract

Let Y be a random variable whose moment generating function exists in some neighborhood of the origin. We consider the probabilistic bivariate Bell polynomials associated with Y and the probabilistic bivariate r-Bell polynomials associated with Y. For those polynomials, we derive the recurrence relations corresponding to the ones found by Zheng and Li for the bivariate Bell polynomials and the bivariate r-Bell polynomials.
Paper Structure (4 sections, 7 theorems, 44 equations)

This paper contains 4 sections, 7 theorems, 44 equations.

Table of Contents

  1. Introduction
  2. Probabilistic bivariate Bell polynomials
  3. Conclusion
  4. Declarations

Key Result

Theorem 2.1

For $n\ge 0$, we have

Theorems & Definitions (7)

  • Theorem 2.1
  • Theorem 2.2
  • Theorem 2.3
  • Theorem 2.4
  • Theorem 2.5
  • Theorem 2.6
  • Theorem 2.7