Limit relations for the complex zeros of Laguerre and q-Laguerre polynomials |
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Authors: | Mark V. DeFazio Martin E. Muldoon |
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Affiliation: | a Algoma University College, Sault Ste. Marie, Ontario P6A 2G4, Canada b Department of Mathematics and Statistics, York University, Toronto, Ontario M3J 1P3, Canada |
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Abstract: | For each the nth Laguerre polynomial has an m-fold zero at the origin when α=−m. As the real variable α→−m, it has m simple complex zeros which approach 0 in a symmetric way. This symmetry leads to a finite value for the limit of the sum of the reciprocals of these zeros. There is a similar property for the zeros of the q-Laguerre polynomials and of the Jacobi polynomials and similar results hold for sums of other negative integer powers. |
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Keywords: | Laguerre polynomials q-Laguerre polynomials Zeros Jacobi polynomials |
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