Jacobi-Sobolev-type orthogonal polynomials: Second-order differential equation and zeros
نویسندگان
چکیده
منابع مشابه
Estimates for Jacobi-sobolev Type Orthogonal Polynomials
Let the Sobolev-type inner product 〈f, g〉 = ∫
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Let dμα,β(x) = (1−x)(1+x)dx, α, β > −1, be the Jacobi measure supported on the interval [−1, 1]. Let us introduce the Sobolev inner product
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where l > 0 and {dk0, dk1} is a so-called symmetrically coherent pair, with dk0 or dk1 the classical Gegenbauer measure (x−1) dx, a > −1. If dk1 is the Gegenbauer measure, then Sn has n different, real zeros. If dk0 is the Gegenbauer measure, then Sn has at least n−2 different, real zeros. Under certain conditions Sn has complex zeros. Also the location of the zeros of Sn with respect to Gegenb...
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Article history: Received 15 December 2008 Available online 3 March 2010 Submitted by D. Waterman
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We consider interlacing properties satisfied by the zeros of Jacobi polynomials in quasi-orthogonal sequences characterised by α > −1, −2 < β < −1. We give necessary and sufficient conditions under which a conjecture by Askey, that the zeros of Jacobi polynomials P (α,β) n and P (α,β+2) n are interlacing, holds when the parameters α and β are in the range α > −1 and −2 < β < −1. We prove that t...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1998
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(98)00005-3