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General Sobolev Orthogonal Polynomials

✍ Scribed by Francisco Marcellán; Teresa E. Pérez; Miguel A. Piñar; André Ronveaux

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
196 KB
Volume
200
Category
Article
ISSN
0022-247X

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✦ Synopsis

In this paper, we study orthogonal polynomials with respect to the inner product Ž . ŽN. ² :

, where G 0 for m s 1, . . . , N, and

u is a semiclassical, positive definite linear functional. For these non-standard orthogonal polynomials, algebraic and differential properties are obtained, as well as their representation in terms of the standard orthogonal polynomials associated with u.

📜 SIMILAR VOLUMES

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✍ Teresa E. Pérez; Miguel A. Piñar 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 359 KB

The orthogonality of the generalized Laguerre polynomials, [L (:) n (x)] n 0 , is a well known fact when the parameter : is a real number but not a negative integer. In fact, for &1<:, they are orthogonal on the interval [0, + ) with respect to the weight function \(x)=x : e &x , and for :<&1, but n

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We investigate orthogonal polynomials for a Sobolev type inner product \(\langle f, g\rangle=(f, g)+\lambda f^{\prime}(c) g^{\prime}(c)\), where \((f, g)\) is an ordinary inner product in \(L_{2}(\mu)\) with \(\mu\) a positive measure on the real line. We compare the Sobolev orthogonal polynomials w