Some Generalized Properties of Poly-Daehee Numbers and Polynomials Based on Apostol–Genocchi Polynomials

Abstract

Numerous polynomial variations and their extensions have been explored extensively and found applications in a variety of research fields. The purpose of this research is to establish a unified class of Apostol–Genocchi polynomials based on poly-Daehee polynomials and to explore some of their features and identities. We investigate these polynomials via generating functions and deduce various identities, summation formulae, differential and integral formulas, implicit summation formulae, and several characterized generating functions for new numbers and polynomials. Finally, by using an operational version of Apostol–Genocchi polynomials, we derive some results in terms of new special polynomials. Due to the generic nature of the findings described here, they are used to reduce and generate certain known or novel formulae and identities for relatively simple polynomials and numbers.

Higher Transcendental Functions and Their Multi-Disciplinary Applications

“…The geographical distribution of the contributors to this Special Issue is remarkably widely-scattered. Their contributions (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]) originated in many different countries on every continent of the world.…”

“…The subject matter of the first 16 publications (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]) dealt extensively with analytic, univalent, multivalent, and harmonic functions of complex analysis and their quantum or basic (or q-) extensions, the Euler-Poisson-Darboux partial differential equation, approximation theory and associated summability methods, variational inequalities, linear and nonlinear integro-differential equations, growth results involving Dirichlet series, theory and applications of wavelet transforms, analysis of ordinary and partial differentialdifference equations, and several other topics listed in the preceding section.…”