Abstract
In this paper, by considering Barnes-type Narumi polynomials of the second kind and Barnes-type Peters polynomials of the second kind, we define and investigate the hybrid polynomials of these polynomials. From the properties of Sheffer sequences of these polynomials arising from umbral calculus, we derive new and interesting identities.
Highlights
In this paper, we consider the polynomialsNSn(x) = NSn(x|a; λ; μ) = NSn(x|a, . . . , ar; λ, . . . , λs; μ, . . . , μs) called Barnes-type Narumi of the second kind and Barnes-type Peters of the second kind hybrid polynomials, whose generating function is given by r i=( + t)ai – ( + t)ai ln( + t) s j=( + t)λj + ( + t)λj μj ( + t)x = ∞ NSn
From the properties of Sheffer sequences of these polynomials arising from umbral calculus, we derive new and interesting identities
L|p(x) is the action of the linear functional L on the polynomial p(x), and we recall that the vector space operations on P∗ are defined by L + M|p(x) = L|p(x) + M|p(x), cL|p(x) = c L|p(x), where c is a complex constant in C
Summary
Μs) called Barnes-type Narumi of the second kind and Barnes-type Peters of the second kind hybrid polynomials, whose generating function is given by r i=. Recall that the Barnes-type Narumi polynomials of the second kind, denoted by Nn(x|a , . By considering Barnes-type Narumi polynomials of the second kind and Barnes-type Peters polynomials of the second kind, we define and investigate the hybrid polynomials of these polynomials. L|p(x) is the action of the linear functional L on the polynomial p(x), and we recall that the vector space operations on P∗ are defined by L + M|p(x) = L|p(x) + M|p(x) , cL|p(x) = c L|p(x) , where c is a complex constant in C. Sheffer sequences are characterized by the generating function of [ , Theorem .
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
