When do linear combinations of orthogonal polynomials yield new sequences of orthogonal polynomials
TLDR
In the case k=2, the families of the sequence of monic orthogonal polynomials {P"n}"n">="0" are characterized such that the corresponding polynmials {Q"n]"n">=0 are also Orthogonal.About:
This article is published in Journal of Computational and Applied Mathematics.The article was published on 2010-01-01 and is currently open access. It has received 38 citations till now. The article focuses on the topics: Function composition & Orthogonal polynomials.read more
Citations
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Orthogonal polynomials associated with an inverse quadratic spectral transform
TL;DR: In this article, the orthogonality of monic orthogonal polynomials with respect to a quasi-definite linear functional was characterized in terms of the coefficients of a quadratic polynomial h such that h(x)v=u.
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Multiple Geronimus transformations
TL;DR: In this article, it was shown that every discrete non-diagonal Sobolev inner product can be obtained as a multiple Geronimus transformation, and a connection with Geronimous spectral transformations for matrix orthogonal polynomials is also considered.
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A note on the Geronimus transformation and Sobolev orthogonal polynomials
TL;DR: This article recast the Geronimus transformation in the framework of polynomials orthogonal with respect to symmetric bilinear forms and showed that the double Geronmus transformations lead to non-diagonal Sobolev type inner products.
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(M,N)-coherent pairs of order (m,k) and Sobolev orthogonal polynomials
TL;DR: This work focuses on the algebraic properties of an (M,N)-coherent pair of order (m,k), and shows how to compute the coefficients of the Fourier expansion of functions on an appropriate Sobolev space (defined by the above inner product) in terms of the sequence of SoboleV orthogonal polynomials {S"n(x;@l)}"n">="0".
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A note on the Geronimus transformation and Sobolev orthogonal polynomials
TL;DR: This note recast the Geronimus transformation in the framework of polynomials orthogonal with respect to symmetric bilinear forms and shows that the doubleGeronimus transformations lead to non-diagonal Sobolev type inner products.
References
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Book
An introduction to difference equations
TL;DR: In this article, the authors combine both analytic and geometric (topological) approaches to studying difference equations and integrate both classical and modern treatments of the subject, offering material stability, z-transform, discrete control theory and symptotic theory.
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The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
Roelof Koekoek,René F. Swarttouw +1 more
TL;DR: The Askey-scheme of hypergeometric orthogonal polynomials was introduced in this paper, where the q-analogues of the polynomial classes in the Askey scheme are given.
Introduction to orthogonal polynomials
TL;DR: In this paper, the authors proposed a model for parameterized t > 0: J− en = √ n(t + n− 1) en−1, J+ en = (n + 1)(t+ n) en+1 + 1, J0 en = n + 2n)en + cJ0 = X
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On mechanical quadratures, in particular, with positive coefficients
TL;DR: Fejfir as discussed by the authors presented a monograph, Theorie generale des polynomes orthogonaux de Tchebycheff (hereafter referred to as M), which was published in 1935.