Novel Properties of q-Sine-Based and q-Cosine-Based q-Fubini Polynomials

Abstract

The main purpose of this paper is to consider q-sine-based and q-cosine-Based q-Fubini polynomials and is to investigate diverse properties of these polynomials. Furthermore, multifarious correlations including q-analogues of the Genocchi, Euler and Bernoulli polynomials, and the q-Stirling numbers of the second kind are derived. Moreover, some approximate zeros of the q-sine-based and q-cosine-Based q-Fubini polynomials in a complex plane are examined, and lastly, these zeros are shown using figures.

A NOTE ON q-ANALOGUE OF CATALAN NUMBERS ASSOCIATED WITH q-CHANGHEE NUMBERS

“…As is well known, the Catalan numbers are defined by the generating function as follows (see [1,2,3,20,21,22,24,25,27])…”

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

“…and the Stirling numbers of the second kind are defined by (see [1][2][3][4][5][6][7][8][9][10][11][12])…”