LIMIT RELATIONS FOR THE COMPLEX ZEROS OF LAGUERRE AND q-LAGUERRE POLYNOMIALS

Abstract

For each m (= 1, . . . , n) the n-th Laguerre polynomial L n (x) 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… (More)

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