Differential Equations Arising from the Generating Function of the (<i>r</i>, <i>β</i>)-Bell Polynomials and Distribution of Zeros of Equations

Abstract

In this paper, we study differential equations arising from the generating function of the ( r , β ) -Bell polynomials. We give explicit identities for the ( r , β ) -Bell polynomials. Finally, we find the zeros of the ( r , β ) -Bell equations with numerical experiments.

Keywords

• differential equations
• Bell polynomials
• <i>r</i>-Bell polynomials
• (<i>r</i>, <i>β</i>)-Bell polynomials
• zeros