Abstract
Since Cauchy numbers were introduced, various types of Cauchy numbers have been presented. In this paper, we define degenerate Cauchy numbers of the third kind and give some identities for the degenerate Cauchy numbers of the third kind. In addition, we give some relations between four kinds of the degenerate Cauchy numbers, the Daehee numbers and the degenerate Bernoulli numbers.
Highlights
The degenerate Cauchy numbers of the second kind, denoted by Cn,λ,2, are introduced in [12] as follows: t tn log(1
It is well known that the Cauchy numbers, denoted by Cn, are derived from the integral as follows: (1 + t)x dx = t log(1 + t) ∞ tn = Cn n! . (1) n=0The Cauchy numbers play a very important role in the study of mathematical physics
1 Introduction It is well known that the Cauchy numbers, denoted by Cn, are derived from the integral as follows: (1 + t)x dx =
Summary
The degenerate Cauchy numbers of the second kind, denoted by Cn,λ,2, are introduced in [12] as follows: t tn log(1 From (8), equation (7) must be related to the Cauchy numbers. We define the degenerate Cauchy numbers of the third kind, denoted by Cn,λ,3, by the generating function λ((1 As λ goes to zero in equation (10), the generating function of the degenerate Cauchy numbers of the forth kind goes to the generating function of the Cauchy numbers, that is, λt t lim λ→0 log(1 + λ log(1 + t)) log(1 + t)
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