The Type 2 Degenerate Hermite-Based Apostol-Frobenius-type Poly-Genocchi Polynomials with Parameters a, b and c
DOI:
https://doi.org/10.29020/nybg.ejpam.v18i3.6167Keywords:
Genocchi polynomials, Bell polynomials, Apostol-type Frobenius-Genocchi polynomials, Hermite-based Apostol-type Frobenius- Genocchi polynomials, degenerate Stirling numbersAbstract
This paper introduces a novel variation of poly-Genocchi polyno- mials by combining elements from the modified degenerate polyexpo- nential function, Hermite-Based Apostol-Genocchi polynomials, and Frobenius polynomials. These newly formulated polynomials, termed as the degenerate Hermite-Based Apostol-Frobenius-type poly-Genocchi polynomials with parameters a, b, and c, are explored to derive various identities and formulas. These include recurrence relations, explicit formulas, and specific differential identities. Furthermore, the pa- per establishes connections between these polynomials and degenerate Stirling numbers of the first and second kind, higher-order degenerate Bernoulli polynomials, and higher-order degenerate Frobenius-Euler polynomials.
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Copyright (c) 2025 Roberto Bagsarsa Corcino, Cristina Corcino
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