On incomplete symmetric orthogonal polynomials of Laguerre type

Abstract

By using the extended Sturm–Liouville theorem for symmetric functions, we introduce the following differential equation:

in which and and show that one of its basis solutions is a class of incomplete symmetric polynomials orthogonal with respect to the weight function on (−∞, ∞). We also obtain the norm square value of this orthogonal class.

Keywords:

• special functions
• extended Sturm–Liouville problems for symmetric functions
• incomplete symmetric orthogonal polynomials of Laguerre type
• weight function
• generalized Hermite polynomials

AMS Subject Classifications::

• 33C45; 05E05; 33C47; 34B24