Bibliographic Details
| Title: |
On the modifications of semi-classical orthogonal polynomials on nonuniform lattices. |
| Authors: |
Mboutngam, S.1 mbsalif@gmail.com, Foupouagnigni, M.2 foupouagnigni@gmail.com, Njionou Sadjang, P.3 pnjionou@yahoo.fr |
| Source: |
Journal of Mathematical Analysis & Applications. Jan2017, Vol. 445 Issue 1, p819-836. 18p. |
| Subjects: |
Orthogonal polynomials, Lattice theory, Linear systems, Multiplication, Mathematical analysis |
| Abstract: |
Semi classical orthogonal polynomials on nonuniform lattices with respect to a linear functional L are defined as polynomials ( P n ) where the degree of P n is exactly n , the P n satisfy the orthogonality relation 〈 L , P n P m 〉 = 0 , n ≠ m , 〈 L , P n P n 〉 ≠ 0 , n ≥ 0 and L satisfies the Pearson equation D x ( ϕ L ) = S x ( ψ L ) , where ϕ is a non zero polynomial and ψ a polynomial of degree at least 1. In this work, we prove that the multiplication of semi classical linear functional by a first degree polynomial, the addition of a Dirac measure to the semi-classical regular linear functional on nonuniform lattice give semi classical linear functional but not necessary of the same class. We apply these modifications to some classical orthogonal polynomials. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
