O q-Integral de Jackson.
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2010
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O q-integral de Jackson tem sido usado para defenir em alguns casos particulares,
relacôes de ortogonalidade entre funcões hipergeometricas basicas. Alguns exemplos podem ser
encontrados nas referencias bibliograficas. Neste trabalho estabelecemos condicoes gerais em a
e b de modo a permitir obter um produto interno definido num espaco (vectorial) apropriado.
Alargamos, tambem, as propriedades conhecidas das fun»c~oes trigonometricas basicas e, alem
de novas demonstracões de propriedades conhecidas dos zeros da Terceira Funcão q-Bessel de
Jackson (ou Funcão q-Bessel de Hahn-Exton), estudamos algumas propriedades duma família
particular de q-polinomios que foram definidos a partir de algumas propriedades conhecidas das
funções trigonometricas basicas numa rede q-linear.
The q-integral of Jackson have been used to define, in some particular cases, orthogo- nality relations among basic hypergeometric functions. Some examples can be found in the bibliographic references. Here we establish general conditions on a and b in order to enable one to obtain an inner-product defined in an appropriated (vectorial) space. We also enlarged the known properties of the basic trigonometric functions and, beyond new proofs on the known properties of the zeros of the Third Jackson q-Bessel Function (or the Hahn-Exton q-Bessel Function), we studied some properties of a particular family of q-polynomials that were defined from some properties of the basic trigonometric functions in a q-linear grid.
The q-integral of Jackson have been used to define, in some particular cases, orthogo- nality relations among basic hypergeometric functions. Some examples can be found in the bibliographic references. Here we establish general conditions on a and b in order to enable one to obtain an inner-product defined in an appropriated (vectorial) space. We also enlarged the known properties of the basic trigonometric functions and, beyond new proofs on the known properties of the zeros of the Third Jackson q-Bessel Function (or the Hahn-Exton q-Bessel Function), we studied some properties of a particular family of q-polynomials that were defined from some properties of the basic trigonometric functions in a q-linear grid.
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Dissertação de Mestrado em Ensino da Matemática