On r-Bell-Based Apostol-Frobenius-Type Poly-Euler Polynomials
DOI:
https://doi.org/10.29020/nybg.ejpam.v18i3.6165Keywords:
Bell polynomials, Apostol-type Frobenius-Euler polynomials, Bell-based Apostol-type Frobenius-Euler polynomials, Stirling numbers, polylogarithmAbstract
This paper introduces a novel variation of Frobenius-Euler poly- nomials derived from Bell numbers and Apostol-type functions, in- corporating the polylogarithm concept. We explore their structure and properties through various analytical methods, with a particular emphasis on generating functions designed for higher-order Apostol- Frobenius-Type Poly-Euler polynomials based on Bell numbers. These functions facilitate the derivation of both explicit and implicit sum- mation formulas. Furthermore, we establish symmetric identities that unveil intricate polynomial relationships. This integration provides a new framework that deepens the understanding and expands the applicability of Poly-Euler polynomials. Our findings contribute to combinatorial and algebraic mathematics, fostering further research in related areas.
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Copyright (c) 2025 Roberto Bagsarsa Corcino, Cristina Corcino, Rodin Paspasan, Ronald Alambra
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