The Spectral Theory of the X1-Laguerre Polynomials
نویسندگان
چکیده
In 2009, Gómez-Ullate, Kamran, and Milson characterized all sequences of polynomials {pn}n=1, with deg pn = n ≥ 1, that are eigenfunctions of a secondorder differential equation and are orthogonal with respect to a positive Borel measure on the real line having finite moments of all orders. Up to a complex linear change of variable, the only such sequences are theX1-Laguerre and theX1-Jacobi polynomials. In this paper, we discuss the self-adjoint operator, generated by the second-order X1-Laguerre differential expression, that has the X1-Laguerre polynomials as eigenfunctions. AMS Subject Classifications: 33C65, 34B20, 47B25.
منابع مشابه
Spectral Theory of X1-Laguerre Polynomials
In 2009, Gómez–Ullate, Kamran, and Milson characterized all sequences of polynomials {pn}n=1, with deg pn = n ≥ 1, that are eigenfunctions of a second– order differential equation and are orthogonal with respect to a positive Borel measure on the real line having finite moments of all orders. Up to a complex linear change of variable, the only such sequences are the X1-Laguerre and the X1-Jacob...
متن کاملExtended Jacobi and Laguerre Functions and their Applications
The aim of this paper is to introduce two new extensions of the Jacobi and Laguerre polynomials as the eigenfunctions of two non-classical Sturm-Liouville problems. We prove some important properties of these operators such as: These sets of functions are orthogonal with respect to a positive de nite inner product de ned over the compact intervals [-1, 1] and [0,1), respectively and also th...
متن کاملApplication of Laguerre Polynomials for Solving Infinite Boundary Integro-Differential Equations
In this study, an efficient method is presented for solving infinite boundary integro-differential equations (IBI-DE) of the second kind with degenerate kernel in terms of Laguerre polynomials. Properties of these polynomials and operational matrix of integration are first presented. These properties are then used to transform the integral equation to a matrix equation which corresponds t...
متن کاملThe Operational matrices with respect to generalized Laguerre polynomials and their applications in solving linear dierential equations with variable coecients
In this paper, a new and ecient approach based on operational matrices with respect to the gener-alized Laguerre polynomials for numerical approximation of the linear ordinary dierential equations(ODEs) with variable coecients is introduced. Explicit formulae which express the generalized La-guerre expansion coecients for the moments of the derivatives of any dierentiable function in termsof th...
متن کاملNumerical solution of Fredholm integral-differential equations on unbounded domain
In this study, a new and efficient approach is presented for numerical solution of Fredholm integro-differential equations (FIDEs) of the second kind on unbounded domain with degenerate kernel based on operational matrices with respect to generalized Laguerre polynomials(GLPs). Properties of these polynomials and operational matrices of integration, differentiation are introduced and are ultili...
متن کامل