P,Q-differentiation, P,Q-integration, and P,Q-hypergeometric functions related to quantum groups

Autor:	U Klimyk Anatoli, M Burban Ivan
Rok vydání:	1994
Předmět:	Pure mathematics Applied Mathematics Discrete orthogonal polynomials Askey–Wilson polynomials Classical orthogonal polynomials symbols.namesake Macdonald polynomials Wilson polynomials Orthogonal polynomials Hahn polynomials symbols Jacobi polynomials Analysis Mathematics
Zdroj:	Integral Transforms and Special Functions. 2:15-36
ISSN:	1476-8291 1065-2469
Popis:	Investigation of representations of two-parametric quantum groups leads to two-parametric differentiation and integration which are generalizations of the well known q-differentiation and q-integration. In this paper these differentiation and integration are studied. Their connection with q-differentiation and q-integration is derived. The p,q-hypergeometric functions are introduced. Their relation to the basic hypergeometric functions is studied. It is emphasized that investigation of some operators of representations of quantum algebras leads to orthogonal polynomials determining their spectral measures and their spectra. Operators of representations of the quantum algebra Upq :(su) and of the p,q-oscillator algebra are studied. Some of these operators lead to unknown orthogonal polynomials. Other ones give particular cases of q-Askey-Wilson polynomials and g-Hermite polynomials with the base r = (pq) 1/2.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::564e46f4ba5319b58aececfeeb7d79f0 https://doi.org/10.1080/10652469408819035 Zobrazit plný text záznamu