Orthogonality of linear combinations of two orthogonal polynomial sequences
نویسندگان
چکیده
منابع مشابه
When do linear combinations of orthogonal polynomials yield new sequences of orthogonal polynomials?
Given {Pn}n≥0 a sequence of monic orthogonal polynomials, we analyze their linear combinations with constant coefficients and fixed length, i.e., Qn(x) = Pn(x) + a1Pn−1(x) + · · ·+ akPn−k, ak 6= 0, n > k. 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 i...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2001
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(00)00702-0