Hankel Determinants of the Generalized Factorials

Sheng-Liang Yang () and Yan-Ni Dong
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Sheng-Liang Yang: Lanzhou University of Technology
Yan-Ni Dong: Lanzhou University of Technology

Indian Journal of Pure and Applied Mathematics, 2018, vol. 49, issue 2, 217-225

Abstract: Abstract Denote 〈x|d〉 n = x(x + d)(x + 2d) · · · (x + (n - 1)d) for n = 1, 2, · · ·, and 〈x|d〉0 = 1, where 〈x|d〉 n is called the generalized factorial of x with increment d. In this paper, we present the evaluation of Hankel determinants of sequence of generalized factorials. The main tool used for the evaluation is the method based on exponential Riordan arrays. Furthermore, we provide Hankel determinant evaluations of the Eulerian polynomials and exponential polynomials.

Keywords: Generalized factorial; Hankel determinant; exponential Riordan array; Eulerian polynomial; exponential polynomial (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s13226-018-0264-9

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