Geodesic
Zeros of Iterated Integrals of Polynomials
Canadian journal of mathematics, Tome 47 (1995) no. 1, pp. 65-87

Voir la notice de l'article provenant de la source Cambridge University Press

The operator Im is defined as m-fold indefinite integration with zero constants of integration. The zero distribution of Im (p) for polynomials p is studied in general, and for two special classes of polynomials in detail. The main results are: (i) The zeros of In (Pn ), where Pn (z) is the n-th Legendre polynomial, converge to a certain algebraic curve; (ii) the zeros of an integer) converge to pieces of a circle and of two "Szegö curves".
DOI : 10.4153/CJM-1995-004-1
Mots-clés : 30C15, 30E15, 33C45, Zeros of polynomials, iterated integrals, Gauss-Lucas theorem, Szegö curve, Legendre polynomials 
Borwein, Peter B.; Chen, Weiyu; Dilcher, Karl. Zeros of Iterated Integrals of Polynomials. Canadian journal of mathematics, Tome 47 (1995) no. 1, pp. 65-87. doi: 10.4153/CJM-1995-004-1
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