On generalized degenerate Gould-Hopper based fully degenerate Bell polynomials

Abstract

In this paper, we introduce both the generalized degenerate Gould-Hopper based degenerate Stirling polynomials of the second kind and the generalized degenerate Gould-Hopper based fully degenerate Bell polynomials. We study and investigate multifarious properties and relations of these polynomials such as explicit formulas, differentiation rules and summation formulas. Moreover, we derive several correlations with the degenerate Bernstein polynomials for these polynomials. Furthermore, we acquire several representations of the generalized degenerate Gould-Hopper based fully degenerate Bell polynomials via not only the fully degenerate Bell polynomials but also the generalized degenerate Gould-Hopper based degenerate Bernoulli, Euler and Genocchi polynomials.