New moment formulas: approach to generating function for Carlitz polynomials in terms of geometric and other probabilistic random variables
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas, vol.120, no.4, 2026 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 120 Issue: 4
- Publication Date: 2026
- Doi Number: 10.1007/s13398-026-01893-7
- Journal Name: Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, MathSciNet, zbMATH, DIALNET, Zoological Record, Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Keywords: Apostol-type polynomials, Binomial coefficients, Carlitz polynomials, Moment generating function, Moments of negative binomial and geometric random variables, Probability distribution, Stirling numbers
- Akdeniz University Affiliated: Yes
Abstract
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.