Zeros of Gegenbauer and Hermite polynomials and connection coefficients

Area, Iván; Dimitrov, Dimitar; Godoy, Eduardo; Ronveaux, André

doi:10.1090/S0025-5718-04-01642-4

Zeros of Gegenbauer and Hermite polynomials and connection coefficients
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by Iván Area, Dimitar K. Dimitrov, Eduardo Godoy and André Ronveaux PDF

Math. Comp. 73 (2004), 1937-1951 Request permission

Abstract:

In this paper, sharp upper limit for the zeros of the ultraspherical polynomials are obtained via a result of Obrechkoff and certain explicit connection coefficients for these polynomials. As a consequence, sharp bounds for the zeros of the Hermite polynomials are obtained.

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