A Family of the <i>r</i>-Associated Stirling Numbers of the Second Kind and Generalized Bernoulli Polynomials

Abstract

In this article, we derive representation formulas for a class of r-associated Stirling numbers of the second kind and examine their connections with a class of generalized Bernoulli polynomials. Herein, we use the Blissard umbral approach and the familiar Bell polynomials. Links with available literature on this subject are also pointed out. The extension to the bivariate case is discussed.

Keywords

• r-associated Stirling numbers
• representation formulas
• Bernoulli polynomials
• Blissard umbral approach
• Bell polynomials
• 2D extensions