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HANKEL DETERMINANTS OF FACTORIAL FRACTIONS

Published online by Cambridge University Press:  07 June 2021

WENCHANG CHU*
Affiliation:
School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou (Henan), PR China and Current address: Department of Mathematics and Physics, University of Salento (P. O. Box 193), 73100 Lecce, Italy

Abstract

By making use of the Cauchy double alternant and the Laplace expansion formula, we establish two closed formulae for the determinants of factorial fractions that are then utilised to evaluate several determinants of binomial coefficients and Catalan numbers, including those obtained recently by Chammam [‘Generalized harmonic numbers, Jacobi numbers and a Hankel determinant evaluation’, Integral Transforms Spec. Funct. 30(7) (2019), 581–593].

Type
Research Article
Copyright
© 2021 Australian Mathematical Publishing Association Inc.

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