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HANKEL DETERMINANTS OF FACTORIAL FRACTIONS

Part of: Numerical linear algebra Basic linear algebra Polynomials and matrices

Published online by Cambridge University Press:  07 June 2021

WENCHANG CHU Open the ORCID record for WENCHANG CHU [Opens in a new window]
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
*
e-mail: chu.wenchang@unisalento.it
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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].

Keywords

Hankel determinantbinomial determinantCauchy double alternantLaplace expansiondivided differencetelescoping methodpartial fraction decomposition

MSC classification

Primary: 15A15: Determinants, permanents, other special matrix functions
Secondary: 11C20: Matrices, determinants 65F40: Determinants

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 105 , Issue 1 , February 2022 , pp. 46 - 57
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Copyright
© 2021 Australian Mathematical Publishing Association Inc.

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