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When do linear combinations of orthogonal polynomials yield new sequences of orthogonal polynomials?

✍ Scribed by Manuel Alfaro; Francisco Marcellán; Ana Peña; M. Luisa Rezola

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
481 KB
Volume
233
Category
Article
ISSN
0377-0427

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✦ Synopsis

Given {P n } n≥0 a sequence of monic orthogonal polynomials, we analyze their linear combinations with constant coefficients and fixed length, i.e.,

Necessary and sufficient conditions are given for the orthogonality of the sequence {Q n } n≥0 . An interesting interpretation in terms of the Jacobi matrices associated with {P n } n≥0 and {Q n } n≥0 is shown.

Moreover, in the case k = 2, we characterize the families {P n } n≥0 such that the corresponding polynomials {Q n } n≥0 are also orthogonal.

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