Combinatorial Identities with Generalized Higher-order Genocchi Sequences

Authors

  • Tian Hao Inner Mongolia University
  • Wuyungaowa Bao Inner Mongolia University

DOI:

https://doi.org/10.29020/nybg.ejpam.v12i2.3403

Keywords:

Moment, Generating function, Generalized higher-order Genocchi numbers and polynomials, Laplace distribution

Keywords:

Moment, Generating function, Generalized higher-order Genocchi numbers and polynomials, Laplace distribution

Abstract

In this paper, we make use of the probabilistic method to calculate the moment representation of generalized higher-order Genocchi polynomials. We obtain the moment expression of the generalized higher-order Genocchi numbers with a and b parameters. Some characteriza tions and identities of generalized higher-order Genocchi polynomials are given by the proof of the moment expression. As far as properties given by predecessors are concerned, we prove them by the probabilistic method. Finally, new identities of relationships involving generalized higher-order Genocchi numbers and harmonic numbers, derangement numbers, Fibonacci numbers, Bell numbers, Bernoulli numbers, Euler numbers, Cauchy numbers and Stirling numbers of the second kind are established.

 

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How to Cite

Hao, T., & Bao, W. (2019). Combinatorial Identities with Generalized Higher-order Genocchi Sequences. European Journal of Pure and Applied Mathematics, 12(2), 605–621. https://doi.org/10.29020/nybg.ejpam.v12i2.3403