3nj-symbols and identities for q-Bessel functions

Wolter Groenevelt

doi:10.1007/s11139-017-9952-z

3nj-symbols and identities for q-Bessel functions

Wolter Groenevelt

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Abstract

The 6j-symbols for representations of the q-deformed algebra of polynomials on SU(2) are given by Jackson’s third q-Bessel functions. This interpretation leads to several summation identities for the q-Bessel functions. Multivariate q-Bessel functions are defined, which are shown to be limit cases of multivariate Askey–Wilson polynomials. The multivariate q-Bessel functions occur as 3nj-symbols.

Original language	English
Pages (from-to)	317–337
Number of pages	21
Journal	The Ramanujan Journal: an international journal devoted to areas of mathematics influenced by Ramanujan
Volume	47
Issue number	2
DOIs	https://doi.org/10.1007/s11139-017-9952-z
Publication status	Published - 2018

Keywords

Jackson’s third q-Bessel function
6j-symbols
3nj-symbols
Multivariate q-Bessel function
Quantum algebra representations

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10.1007/s11139-017-9952-z

s11139-017-9952-zFinal published version, 519 KBLicence: CC BY

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abstract = "The 6j-symbols for representations of the q-deformed algebra of polynomials on SU(2) are given by Jackson{\textquoteright}s third q-Bessel functions. This interpretation leads to several summation identities for the q-Bessel functions. Multivariate q-Bessel functions are defined, which are shown to be limit cases of multivariate Askey–Wilson polynomials. The multivariate q-Bessel functions occur as 3nj-symbols.",

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AB - The 6j-symbols for representations of the q-deformed algebra of polynomials on SU(2) are given by Jackson’s third q-Bessel functions. This interpretation leads to several summation identities for the q-Bessel functions. Multivariate q-Bessel functions are defined, which are shown to be limit cases of multivariate Askey–Wilson polynomials. The multivariate q-Bessel functions occur as 3nj-symbols.

KW - Jackson’s third q-Bessel function

KW - 6j-symbols

KW - 3nj-symbols

KW - Multivariate q-Bessel function

KW - Quantum algebra representations

U2 - 10.1007/s11139-017-9952-z

DO - 10.1007/s11139-017-9952-z

M3 - Article

SN - 1382-4090

VL - 47

SP - 317

EP - 337

JO - The Ramanujan Journal: an international journal devoted to areas of mathematics influenced by Ramanujan

JF - The Ramanujan Journal: an international journal devoted to areas of mathematics influenced by Ramanujan

IS - 2

ER -

3nj-symbols and identities for q-Bessel functions

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