Combinatorial Identities with Several Kinds of Degenerate-Daehee Sequences

Tian Hao; . Wuyungaowa

Tian Hao Department of Mathematical Sciences, Inner Mongolia University, 235 West Daxue Road, Inner Mongolia, China
. Wuyungaowa Department of Mathematical Sciences, Inner Mongolia University, 235 West Daxue Road, Inner Mongolia, China

Keywords: Moment, Generating function, Degenerate Daehee numbers of the third kind, Uniform distribution, Gamma distribution.

Abstract

In this paper, we mainly make use of the probabilistic method to calculate several different moment representations of the degenerate Daehee numbers of the third kind with degenerate log function. We also obtain the moment expressions of the degenerate Daehee numbers of higher-order and degenerate Daehee numbers of the second kind. When deriving the moment representations of degenerate Stirling numbers and the degenerate Bernoulli numbers, we arrive at the combinatorial identities of relationships of them and we prove them by the probabilistic method.

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