Riordan arrays and r-Stirling number identities

Ma, Qiang; Wang, Weiping

doi:10.1016/j.disc.2022.113211

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction2

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2023

Publication Types

Select...

Article2

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

(2 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For convenience and notational simplicity, in this paper we employ the notation k . The former notation has been used recently by Ma and Wang in [13] (see also [1] and [14]). The numbers k j r are then given by…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Sums of Powers of Integers and Stirling Numbers

Cereceda¹

2022

Reson

View full text Add to dashboard Cite

By applying the Newton-Gregory expansion to the polynomial associated with the sum of powers of integerswe derive a couple of infinite families of explicit formulas for S k (n). One of the families involves the r-Stirling numbers of the second kind k j r , j = 0, 1, . . . , k, while the other involves their duals k j −r , with both families of formulas being indexed by the non-negative integer r. As a by-product, we obtain three additional formulas for S k (n) in terms of the numbers k j n+m , k j n−m (where m is any given non-negative integer), and k j k−j , respectively. Moreover, we provide a pair of formulas for the Bernoulli polynomials B k (x) involving the numbers k j x .

show abstract

Section: Introductionmentioning

confidence: 99%

“…Likewise, adopting the notation in [13], we define the counterpart or dual of k j r for negative integer r as…”

Section: Introductionmentioning

confidence: 99%