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A new property of a class of Jacobi polynomials |
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| Authors: | George Csordas Marios Charalambides Fabian Waleffe |
| Affiliation: | Department of Mathematics, University of Hawaii, Honolulu, Hawaii 96822 ; Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706 ; Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706 |
| Abstract: | Polynomials whose coefficients are successive derivatives of a class of Jacobi polynomials evaluated at  are stable. This yields a novel and short proof of the known result that the Bessel polynomials are stable polynomials. Stability-preserving linear operators are discussed. The paper concludes with three open problems involving the distribution of zeros of polynomials. |
| Keywords: | Jacobi and Bessel polynomials stability real zeros of polynomials |
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