General Odd and Even Central Factorial Polynomial Sequences

Abstract

The δ2(·) operator, where δ(·) is the known central difference operator, is considered. The associated odd and even polynomial sequences are determined and their generalizations studied. Particularly, matrix and determinant forms, recurrence formulas, generating functions and an algorithm for effective calculation are provided. An interesting property of biorthogonality is also demonstrated. New examples of odd and even central polynomial sequences are given.

Keywords

• polynomial sequences
• central factorial polynomials
• odd and even polynomials
• discrete operators
• Hessenberg determinant
• recurrence