In this paper, we study the quasi-orthogonality of orthogonal polynomials. New results on the location of their zeros are given in two particular cases. Then these results are applied to Gegenbauer, Jacobi and Laguerre polynomials when the restrictions on the parameters involved in their definitions are not satisfied. The corresponding weight functions are investigated and the location of their zeros is discussed.
Quasi-orthogonality with applications to some families of classical orthogonal polynomials
REDIVO ZAGLIA, MICHELA
2004
Abstract
In this paper, we study the quasi-orthogonality of orthogonal polynomials. New results on the location of their zeros are given in two particular cases. Then these results are applied to Gegenbauer, Jacobi and Laguerre polynomials when the restrictions on the parameters involved in their definitions are not satisfied. The corresponding weight functions are investigated and the location of their zeros is discussed.
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