The distribution of zeros of a class of Jacobi polynomials

Charalambides, Marios; Csordas, George

doi:10.1090/S0002-9939-2010-10436-7

The distribution of zeros of a class of Jacobi polynomials
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by Marios Charalambides and George Csordas PDF

Proc. Amer. Math. Soc. 138 (2010), 4345-4357 Request permission

Abstract:

Polynomials whose coefficients are successive derivatives of a class of generalized Laguerre polynomials evaluated at $x=0$ are shown to be stable. These polynomials can be expressed in terms of Jacobi polynomials. The authors also prove that a related family of polynomials, depending on a parameter, possess only real and negative zeros. A special class of stability-preserving operators is also investigated.

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