Non-classical orthogonality relations for big and little q-Jacobi polynomials
- Moreno, Samuel G.
- García-Caballero, Esther M.
DOIAbstract
AbstractBig q-Jacobi polynomials {Pn(⋅;a,b,c;q)}n=0∞ are classically defined for 0<a<q−1, 0<b<q−1 and c<0. For the family of little q-Jacobi polynomials {pn(⋅;a,b|q)}n=0∞, classical considerations restrict the parameters imposing 0<a<q−1 and b<q−1. In this work we extend both families in such a way that wider sets of parameters are allowed, and we establish orthogonality conditions for those cases for which Favard’s theorem does not work. As a by-product, we obtain similar results for the families of big and little q-Laguerre polynomials
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