q-SOBOLEV ORTHOGONALITY OF THE q-LAGUERRE POLYNOMIALS <수식> FOR POSITIVE INTEGERS N
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초록
The family of q-Laguerre polynomials <수식> is usually defined for 0 < q < 1 and α > -1. We extend this family to a new one in which arbitrary complex values of the parameter α are allowed. These so-called generalized q-Laguerre polynomials fulfil the same three term recurrence relation as the original ones, but when the parameter α is a negative integer, no orthogonality property can be deduced from Favard's theorem. In this work we introduce non-standard inner products involving q-derivatives with respect to which the generalized q-Laguerre polynomials <수식>, for positive integers N, become orthogonal.
Abstract
The family of q-Laguerre polynomials <수식> is usually defined for 0 < q < 1 and α > -1. We extend this family to a new one in which arbitrary complex values of the parameter α are allowed. These so-called generalized q-Laguerre polynomials fulfil the same three term recurrence relation as the original ones, but when the parameter α is a negative integer, no orthogonality property can be deduced from Favard's theorem. In this work we introduce non-standard inner products involving q-derivatives with respect to which the generalized q-Laguerre polynomials <수식>, for positive integers N, become orthogonal.
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