EXTENDED APOSTOL-TYPE (λ-ARRAY) CENTRAL FACTORIAL NUMBERS AND POLYNOMIALS OF THE SECOND KIND

In this study, we first consider extended Apostol-type central factorial numbers of the second kind. We then develop several of their properties and formulas, such as explicit formulas, summation formulas, and addition formulas. Then we get diverse summation formulas related to the Apostol-type Stirling numbers of the second kind. Afterthat, we define one-variable extended Apostol-type central factorial polynomials of the second kind and examine some of their relations and properties, such as addition formula, summation formulas, and recurrence relation. We also find some correlations with the Apostol-type Stirling numbers and polynomials of the second kind. Moreover, we determine a derivative property and an integral representation of the extended Apostol-type central factorial polynomials of the second kind.