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
A note on Sobolev orthogonality for Laguerre matrix polynomials
✍ Scribed by Zhihui Zhu; Zhongkai Li
- Publisher
- Springer
- Year
- 2007
- Tongue
- English
- Weight
- 59 KB
- Volume
- 23
- Category
- Article
- ISSN
- 1573-8175
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
Let fS n g denote the sequence of polynomials orthogonal with respect to the Sobolev inner product ðf ; gÞ S ¼ where a4 À 1; l40 and the leading coefficient of the S n is equal to the leading coefficient of the Laguerre polynomial L ðaÞ n : In this work, a generating function for the Sobolev-Laguer
Let {S,} denote the sequence of polynomials orthogonal with respect to the Sobolev inner product fo +°° f+°c :,. x . ,.x--%-X dx (f.g)s = f(x)o(x)x%-Xdx + 2 J ~ )9( )x . ## JO where ~ > -1, 2 > 0 and the leading coefficient of the S~ is equal to the leading coefficient of the Laguerre polynomial
In this paper we study the asymptotic behaviour of polynomials orthogonal with respect to a Sobolev-type inner product where p and q are polynomials with real coefficients, and A is a positive semidefinite matrix. We will focus our attention on their outer relative asymptotics with respect to the
We prove that the zeros of a certain family of Sobolev orthogonal polynomials involving the Freud weight function e -x 4 on R are real, simple, and interlace with the zeros of the Freud polynomials, i.e., those polynomials orthogonal with respect to the weight function e -x 4 . Some numerical examp