Abstract
We firstly consider the fully degenerate Gould–Hopper polynomials with a q parameter and investigate some of their properties including difference rule, inversion formula and addition formula. We then introduce the Gould–Hopper-based fully degenerate poly-Bernoulli polynomials with a q parameter and provide some of their diverse basic identities and properties including not only addition property, but also difference rule properties. By the same way of mentioned polynomials, we define the Gould–Hopper-based fully degenerate ( α , q ) -Stirling polynomials of the second kind, and then give many relations. Moreover, we derive multifarious correlations and identities for foregoing polynomials and numbers, including recurrence relations and implicit summation formulas.
Highlights
Special functions possess a lot of importances in numerous fields of mathematics, physics, engineering and other related disciplines covering different topics such as differential equations, mathematical analysis, functional analysis, mathematical physics, quantum mechanics and so on
Araci et al [4] considered a novel concept of the Apostol Hermite-Genocchi polynomials by using the modified Milne–Thomson’s polynomials and obtained several implicit summation formulae and general symmetric identities arising from different analytical means and generating functions method
We examine some special cases of the fully degenerate Gould–Hopper polynomials with a q parameter as follows
Summary
Special functions possess a lot of importances in numerous fields of mathematics, physics, engineering and other related disciplines covering different topics such as differential equations, mathematical analysis, functional analysis, mathematical physics, quantum mechanics and so on. Dattoli et al [9] applied the method of generating function to define novel forms of Bernoulli numbers and polynomials, which were. Ozarslan provided explicit closed-form formulae for this unified family and proved a finite series relation between this unification and 3d-Hermite polynomials. Let f ( x ) be a polynomial of degree N, the following Taylor formula holds true: N f (x) =.
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