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Cited 25 time in webofscience Cited 31 time in scopus
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Degenerate binomial coefficients and degenerate hypergeometric functionsopen access

Authors
Kim, TaekyunKim, Dae SanLee, HyunseokKwon, Jongkyum
Issue Date
12-Mar-2020
Publisher
SPRINGEROPEN
Keywords
Degenerate hypergeometric function; Degenerate bivariate Bell polynomials; Degenerate hypergeometric numbers of order p; lambda-Hypergeometric numbers of order p
Citation
ADVANCES IN DIFFERENCE EQUATIONS, v.2020, no.1
Indexed
SCIE
SCOPUS
Journal Title
ADVANCES IN DIFFERENCE EQUATIONS
Volume
2020
Number
1
URI
https://scholarworks.gnu.ac.kr/handle/sw.gnu/6822
DOI
10.1186/s13662-020-02575-3
ISSN
1687-1839
1687-1847
Abstract
In this paper, we investigate degenerate versions of the generalized pth order Franel numbers which are certain finite sums involving powers of binomial coefficients. In more detail, we introduce degenerate generalized hypergeometric functions and study degenerate hypergeometric numbers of order p. These numbers involve powers of lambda-binomial coefficients and lambda-falling sequence, and can be represented by means of the degenerate generalized hypergeometric functions. We derive some explicit expressions and combinatorial identities for those numbers. We also consider several related special numbers like lambda-hypergeometric numbers of order p and Apostol type lambda-hypergeometric numbers of order p, of which the latter reduce in a limiting case to the generalized pth order Franel numbers.
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