Three Determinant Evaluations

Three Determinant Evaluations

By means of matrix decompositions, three determinants with their entries being binomial sums are evaluated in closed forms. Ten remarkable examples are illustrated as propositions, which present determinant identities about binomial coefficients and quotients of rising factorials, as well as orthogo...

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Veröffentlicht in:Bulletin of the Malaysian Mathematical Sciences Society 2021-05, Vol.44 (3), p.1691-1700
Hauptverfasser: Chu, Wenchang, Kılıç, Emrah
Format: Artikel
Sprache:eng
Schlagworte:
Applications of Mathematics
Binomial coefficients
Factorials
Hermite polynomials
Mathematics
Mathematics and Statistics
Quotients
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Beschreibung
Zusammenfassung:By means of matrix decompositions, three determinants with their entries being binomial sums are evaluated in closed forms. Ten remarkable examples are illustrated as propositions, which present determinant identities about binomial coefficients and quotients of rising factorials, as well as orthogonal polynomials named after Hermite, Laguerre and Legendre.
ISSN:0126-6705
2180-4206
DOI:10.1007/s40840-020-01005-7