Explicit expressions for a family of Bell polynomials and derivatives of some functions
arXiv:1404.6734 · doi:10.1016/j.amc.2015.02.027
Abstract
In the paper, the authors first inductively establish explicit formulas for derivatives of the arc sine function, then derive from these explicit formulas explicit expressions for a family of Bell polynomials related to the square function, and finally apply these explicit expressions to find explicit formulas for derivatives of some elementary functions.
16 pages