Prather, Carl L.2017-09-182017-09-182001-01-01Carl Prather, “On the number of zeros of iterated operators on analytic Legendre expansions,” International Journal of Mathematics and Mathematical Sciences, vol. 28, no. 8, pp. 461-467, 2001. doi:10.1155/S0161171201006056http://hdl.handle.net/10919/79107Let L=(1−z2)D2−2zD, D=d/dz and f(z)=∑n=0∞cnpn(z), with Pn being the nth Legendre polynomialand f analytic in an ellipse with foci ±1. Set Lk=L(Lk−1), k≥2. Then the number of zeros of Lkf(z) in this ellipse is O(klnk).application/pdfenCreative Commons Attribution 4.0 InternationalArticle - Refereed2017-09-18Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.https://doi.org/10.1155/S0161171201006056