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<p>Main goal of this paper is to construct generating function for Carlitz polynomials of higher order and moment generating functions related to the negative binomial and geometric distributions. Using these functions, we derive many novel moment formulas. Applying probabilistic random variables to this generating function, we also derive many new formulas of the Carlitz polynomials of higher order. Furthermore, we define probabilistic Carlitz polynomials of higher order. These polynomials involve the Poisson distribution and the Bernoulli distribution.</p>

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New moment formulas: approach to generating function for Carlitz polynomials in terms of geometric and other probabilistic random variables

  • 期刊论文

  • 发表日期：

    2026年7月9日

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  • Neslihan Kilar,
  • Buket Simsek

摘要

Main goal of this paper is to construct generating function for Carlitz polynomials of higher order and moment generating functions related to the negative binomial and geometric distributions. Using these functions, we derive many novel moment formulas. Applying probabilistic random variables to this generating function, we also derive many new formulas of the Carlitz polynomials of higher order. Furthermore, we define probabilistic Carlitz polynomials of higher order. These polynomials involve the Poisson distribution and the Bernoulli distribution.