Degenerate binomial coefficients and degenerate hypergeometric functionsopen access
- Kim, Taekyun; Kim, Dae San; Lee, Hyunseok; Kwon, Jongkyum
- Issue Date
- Degenerate hypergeometric function; Degenerate bivariate Bell polynomials; Degenerate hypergeometric numbers of order p; lambda-Hypergeometric numbers of order p
- ADVANCES IN DIFFERENCE EQUATIONS, v.2020, no.1
- Journal Title
- ADVANCES IN DIFFERENCE EQUATIONS
- 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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- 사범대학 > 수학교육과 > Journal Articles
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