On Polynomial Solutions of a Class of Linear Differential Equations of the Second Order

Authors

W. C. Brenke, University of Nebraska - Lincoln

Document Type

Article

Date of this Version

1930

Comments

Published in Bull. Amer. Math. Soc. 36 (1930) 77-84.

Abstract

Certain well known polynomials have a number of common properties. They arise as coefficients of tⁿ in the expansion of a generating function ; they may be obtained by means of orthogonalization of a set of functions xⁿg(x) when the function ρ(x) = g²(x) and the interval are properly chosen ; they may be regarded as polynomials which become orthogonal when multiplied by a proper factor g(x) ; they satisfy a certain type of difference equation ; they satisfy a certain type of differential equation. The results of this paper are based on the differential equation. Some of them are general statements of results already known for various classes of polynomials; others are believed to be new.