Relationships between identities for quantum bernstein bases and formulas for hypergeometric series

Fatma Zürnacı; Ron Goldman; Plamen Simeonov

doi:10.2298/FIL2008485Z

Relationships between identities for quantum bernstein bases and formulas for hypergeometric series

Fatma Zürnacı, Ron Goldman, Plamen Simeonov

Department of Mathematics Engineering

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

Two seemingly disparate mathematical entities – quantum Bernstein bases and hypergeometric series – are revealed to be intimately related. The partition of unity property for quantum Bernstein bases is shown to be equivalent to the Chu-Vandermonde formula for hypergeometric series, and the Marsden identity for quantum Bernstein bases is shown to be equivalent to the Pfaff-Saalschütz formula for hypergeometric series. The equivalence of the q-versions of these formulas and identities is also demonstrated.

Original language	English
Pages (from-to)	2485-2494
Number of pages	10
Journal	Filomat
Volume	34
Issue number	8
DOIs	https://doi.org/10.2298/FIL2008485Z
Publication status	Published - 2020

Bibliographical note

Publisher Copyright:
© 2020, University of Nis. All rights reserved.

Keywords

Chu-Vandermonde formula
Hypergeometric series
Marsden identity
Pfaff-Saalschütz formula
Quantum Bernstein bases

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10.2298/FIL2008485Z

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abstract = "Two seemingly disparate mathematical entities – quantum Bernstein bases and hypergeometric series – are revealed to be intimately related. The partition of unity property for quantum Bernstein bases is shown to be equivalent to the Chu-Vandermonde formula for hypergeometric series, and the Marsden identity for quantum Bernstein bases is shown to be equivalent to the Pfaff-Saalsch{\"u}tz formula for hypergeometric series. The equivalence of the q-versions of these formulas and identities is also demonstrated.",

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AU - Simeonov, Plamen

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AB - Two seemingly disparate mathematical entities – quantum Bernstein bases and hypergeometric series – are revealed to be intimately related. The partition of unity property for quantum Bernstein bases is shown to be equivalent to the Chu-Vandermonde formula for hypergeometric series, and the Marsden identity for quantum Bernstein bases is shown to be equivalent to the Pfaff-Saalschütz formula for hypergeometric series. The equivalence of the q-versions of these formulas and identities is also demonstrated.

KW - Chu-Vandermonde formula

KW - Hypergeometric series

KW - Marsden identity

KW - Pfaff-Saalschütz formula

KW - Quantum Bernstein bases

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ER -

Relationships between identities for quantum bernstein bases and formulas for hypergeometric series

Abstract

Bibliographical note

Keywords

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