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Hankel Determinants of the Generalized Factorials

Indian Journal of Pure and Applied Mathematics, ISSN: 0975-7465, Vol: 49, Issue: 2, Page: 217-225
2018
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Denote 〈x|d〉 = x(x + d)(x + 2d) · · · (x + (n - 1)d) for n = 1, 2, · · ·, and 〈x|d〉 = 1, where 〈x|d〉 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.

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