SYMMETRIC IDENTITIES FOR DEGENERATE q-POLY-GENOCCHI NUMBERS AND POLYNOMIALS

Nadeem, Mohd; Khan, Waseem A.

doi:10.56827/seajmms.2023.1901.2

SEAJMMS

2023

DOI: 10.56827/seajmms.2023.1901.2

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SYMMETRIC IDENTITIES FOR DEGENERATE q-POLY-GENOCCHI NUMBERS AND POLYNOMIALS

Mohd Nadeem¹,

Waseem A. Khan²

Abstract: In the present article, we introduce a new class of degenerate q-poly- Genocchi polynomials and numbers including q-logarithm function. We derive some relations with this polynomials and the Stirling numbers of the second kind and investigate some symmetric identities using special functions that are involving these polynomials

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Some Explicit Properties of Frobenius–Euler–Genocchi Polynomials with Applications in Computer Modeling

et al. 2023

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Many properties of special polynomials, such as recurrence relations, sum formulas, and symmetric properties, have been studied in the literature with the help of generating functions and their functional equations. In this study, we define Frobenius–Euler–Genocchi polynomials and investigate some properties by giving many relations and implementations. We first obtain different relations and formulas covering addition formulas, recurrence rules, implicit summation formulas, and relations with the earlier polynomials in the literature. With the help of their generating function, we obtain some new relations, including the Stirling numbers of the first and second kinds. We also obtain some new identities and properties of this type of polynomial. Moreover, using the Faà di Bruno formula and some properties of the Bell polynomials of the second kind, we obtain an explicit formula for the Frobenius–Euler polynomials of order α. We provide determinantal representations for the ratio of two differentiable functions. We find a recursive relation for the Frobenius–Euler polynomials of order α. Using the Mathematica program, the computational formulae and graphical representation for the aforementioned polynomials are obtained.

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Some Explicit Properties of Frobenius–Euler–Genocchi Polynomials with Applications in Computer Modeling

et al. 2023

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SYMMETRIC IDENTITIES FOR DEGENERATE q-POLY-GENOCCHI NUMBERS AND POLYNOMIALS

Cited by 1 publication

References 20 publications

Some Explicit Properties of Frobenius–Euler–Genocchi Polynomials with Applications in Computer Modeling

Some Explicit Properties of Frobenius–Euler–Genocchi Polynomials with Applications in Computer Modeling

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