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Probabilistic degenerate Fubini polynomials associated with random variables

Rongrong Xu, Taekyun Kim, Dae San Kim, Yuankui Ma

Abstract

Let Y be a random variable such that the moment generating function of Y exists in a neighborhood of the origin. The aim of this paper is to study probabilistic versions of the degenerate Fubini polynomials and the degenerate Fubini polynomials of order $r$, namely the probabilisitc degenerate Fubini polynomials associated with Y and the probabilistic degenerate Fubini polynomials of order r associated with Y. We derive some properties, explicit expressions, certain identities and recurrence relations for those polynomials.

Probabilistic degenerate Fubini polynomials associated with random variables

Abstract

Let Y be a random variable such that the moment generating function of Y exists in a neighborhood of the origin. The aim of this paper is to study probabilistic versions of the degenerate Fubini polynomials and the degenerate Fubini polynomials of order , namely the probabilisitc degenerate Fubini polynomials associated with Y and the probabilistic degenerate Fubini polynomials of order r associated with Y. We derive some properties, explicit expressions, certain identities and recurrence relations for those polynomials.
Paper Structure (3 sections, 16 theorems, 75 equations)

This paper contains 3 sections, 16 theorems, 75 equations.

Table of Contents

  1. Introduction
  2. Probabilistic degenerate Fubini polynomials associated with random variables
  3. Conclusion

Key Result

Theorem 1

For $n\ge 0$, we have

Theorems & Definitions (16)

  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Theorem 4
  • Theorem 5
  • Theorem 6
  • Theorem 7
  • Theorem 8
  • Theorem 9
  • Theorem 10
  • ...and 6 more