Cita:
Rocky Mountain Journal of Mathematics, 2010 (In press)
ISSN:
0035-7596
Agradecimientos:
Research by first author (H.P.) was partially supported by Dirección General de Investigación, Ministerio de Ciencia y Tecnología de España, under grant MTM2006-13000-C03-02, by Comunidad de Madrid-Universidad Carlos III de Madrid, under grant CCG06-UC3M/EST-0690 and by Centro de Investigación Matemática de Canarias (CIMAC). Research by second author (J.Y.B.) was supported by CNPq-TWAS. Research by third author (W.U.) was partially supported by Centro de Investigación Matemática de Canarias (CIMAC).
We introduce a new class of polynomials {Pn}, that we call polar Legendre polynomials, they appear as solutions of an inverse Gauss problem of equilibrium
position of a field of forces with n + 1 unit masses. We study algebraic, differential
and asymptotic pWe introduce a new class of polynomials {Pn}, that we call polar Legendre polynomials, they appear as solutions of an inverse Gauss problem of equilibrium
position of a field of forces with n + 1 unit masses. We study algebraic, differential
and asymptotic properties of this class of polynomials, that are simultaneously
orthogonal with respect to a differential operator and a discrete-continuous Sobolev
type inner product.[+][-]
Nota:
10 pages, no figures.-- MSC2000 codes: Primary 42C05; Secondary 33C25.-- ArXiv pre-print available at: http://arxiv.org/abs/0709.4537
Accepted in Rocky Mountain Journal of Mathematics.
