A basic class of symmetric orthogonal polynomials of a discrete variable

作者：Masjed Jamei Mohammad; Area Ivan^*

来源：Journal of Mathematical Analysis and Applications, 2013, 399(1): 291-305.

DOI：10.1016/j.jmaa.2012.10.020

• Extended Sturm-Liouville theorem for symmetric functions of a discrete variable
• Classical symmetric orthogonal polynomials of a discrete variable
• Hypergeometric series
• Symmetric Kravchuk and Hahn-Eberlein polynomials

By using a generalization of Sturm-Liouville problems in discrete spaces, a basic class of symmetric orthogonal polynomials of a discrete variable with four free parameters, which generalizes all classical discrete symmetric orthogonal polynomials, is introduced. The standard properties of these polynomials, such as a second order difference equation, an explicit form for the polynomials, a three term recurrence relation and an orthogonality relation are presented. It is shown that two hypergeometric orthogonal sequences with 20 different weight functions can be extracted from this class. Moreover, moments corresponding to these weight functions can be explicitly computed. Finally, a particular example containing all classical discrete symmetric orthogonal polynomials is studied in detail.

• 出版日期2013-3-1