𝔖 Bobbio Scriptorium
✦   LIBER   ✦

An asymptotic result for Laguerre-Sobolev orthogonal polynomials

✍ Scribed by Francisco Marcellán; Henk G Meijer; Teresa E Pérez; Miguel A Piñar

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
266 KB
Volume
87
Category
Article
ISSN
0377-0427

No coin nor oath required. For personal study only.

✦ Synopsis

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 L~ ~). Then, if xEC[0. +o¢).

lim S.(x)

.~o~ L~-~)(x) is a constant depending on 2.

📜 SIMILAR VOLUMES

Laguerre-Sobolev orthogonal polynomials
Laguerre-Sobolev orthogonal polynomials
✍ Francisco Marcellán; Teresa E. Pérez; Miguel A. Piñar 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 871 KB
Asymptotic behaviour of Laguerre–Sobolev
Asymptotic behaviour of Laguerre–Sobolev-type orthogonal polynomials. A nondiagonal case
✍ Herbert Dueñas; Francisco Marcellán 📂 Article 📅 2010 🏛 Elsevier Science 🌐 English ⚖ 237 KB

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

A generating function for Laguerre–Sobol
A generating function for Laguerre–Sobolev orthogonal polynomials
✍ H.G. Meijer; M.A. Piñar 📂 Article 📅 2003 🏛 Elsevier Science 🌐 English ⚖ 155 KB

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

On Sobolev Orthogonality for the General
On Sobolev Orthogonality for the Generalized Laguerre Polynomials
✍ 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