RT Journal Article
T1 When do linear combinations of orthogonal polynomials yield new sequences of orthogonal polynomials?
A1 Alfaro, Manuel
A1 Marcellán Español, Francisco José
A1 Peña, Ana
A1 Rezola, M. Luisa
AB Given {Pn}n≥0 a sequence of monic orthogonal polynomials, we analyze their linear combinations with constant coefficients and fixed length, i.e.,
AB Qn(x) = Pn(x) + a1Pn-1(x) + ... + akPn-k(x), ak<>0, n>k.
AB Necessary and sufficient conditions are given for the orthogonality of the sequence {Qn}n≥0. An interesting interpretation in terms of the Jacobi matrices associated with {Pn}n≥0 and {Qn}n≥0 is shown.
PB Elsevier
SN 0377-0427
YR 2010
FD 2010-01
LK https://hdl.handle.net/10016/5900
UL https://hdl.handle.net/10016/5900
LA eng
NO 7 pages, no figures.-- MSC2000 codes: 33C45; 42C05.-- Issue title: "Special Functions, Information Theory, and Mathematical Physics" (Special issue dedicated to Professor Jesús Sánchez Dehesa on the occasion of his 60th birthday).
NO MA and MLR partially supported by Ministerio de Educación y Ciencia (MEC) of Spain under Grant MTM 2006-13000-C03-03 and Diputación General de Aragón (DGA) project E-64. FM partially supported by MEC of Spain under Grant MTM 2006-13000-C03-02 and INTAS Research Network NeCCA 03-51-6637. AP partially supported by MEC of Spain under Grants MTM 2004-03036 and MTM 2006-13000-C03-03 and DGA project E-64.
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