Abstract
In this paper, we study the Barnes-type Narumi polynomials with umbral calculus viewpoint. From our study, we derive various identities of the Barnes-type Narumi polynomials.MSC:05A19, 05A40, 11B68.
Highlights
As is well known, the Narumi polynomials of order α are defined by the generating function to be t log( + t) α ( + t)x = ∞ Nn(α)(x) tn n!. ( ) n=Let r ∈ Z>
We study the Barnes-type Narumi polynomials with umbral calculus viewpoint
Where Hm(s)(x|λ) are the Frobenius-Euler polynomials of order s defined by the generating function as
Summary
The Narumi polynomials of order α are defined by the generating function to be t log( + t). We consider the polynomials Nn(x|a , . Ar), respectively, called the Barnes-type Narumi polynomials of the first kind and those of the second kind and respectively given by r ( + t)aj – log( + t). Ar) are respectively called the Barnes-type Narumi numbers of the first kind and those of the second kind
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