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Previous issue date: 2018-05-24 === Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) === O objetivo desta dissertação é estudar os chamados polinômios q-ortogonais. Com esse objetivo, analisamos algumas das igualdades envolvendo q-fatoriais, séries q-hipergeométricas e suas aplicações em certos polinômios q-ortogonais. Os resultados estão associados a quatro casos particulares de polinômios q-ortogonais, q-Hermite, q-Ultra-esféricos, Al-Salam-Chihara e Askey-Wilson, os quais são bastante explorados. === The objective of this dissertation is to consider a study of the so-called q-orthogonal polynomials. With this objective we look at some of the equalities involving qfatorials,q-hypergeometric series and their applications towards certain q-orthogonal polynomials. Results are associated with four particular cases of q-orthogonal polynomials,namely: theq-Hermite, q-Ultraespherical, Al-Salam-Chihara and the AskeyWilson, which thouroughly explored.
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