(p, q)-Rogers-Szegö Polynomial and the (p, q)-Oscillator

Ramaswamy Jagannathan () and Raghavendra Sridhar ()
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Ramaswamy Jagannathan: Chennai Mathematical Institute
Raghavendra Sridhar: The Institute of Mathematical Sciences

A chapter in The Legacy of Alladi Ramakrishnan in the Mathematical Sciences, 2010, pp 491-501 from Springer

Abstract: Summary A (p,q)-analog of the classical Rogers-Szegö polynomial is defined by replacing the q-binomial coefficient in it by the (p,q)-binomial coefficient corresponding to the definition of (p,q)-number as $${[n]}_{p,q} = ({p}^{n} - {q}^{n})/(p - q)$$ . Exactly like the Rogers-Szegö polynomial is associated with the q-oscillator algebra, the (p,q)-Rogers-Szegö polynomial is found to be associated with the (p,q)-oscillator algebra.

Keywords: q-hypergeometric series; (p; q)-hypergeometric series; q-special functions; (p; q)-special functions; q-binomial coefficients; Rogers-Szegö polynomial; (p; q)-binomial coefficients; (p; q)-Rogers-Szegö polynomial; quantum groups; q-oscillator; (p; q)-oscillator; (p; q)-Steiltjes-Wigert polynomial; continuous (p; q)-Hermite polynomial (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4419-6263-8_29

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DOI: 10.1007/978-1-4419-6263-8_29

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