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
Cited by in corpus (4)
- Maclaurin's series expansions for positive integer powers of inverse (hyperbolic) sine and related functions, specific values of partial Bell polynomials, and two applications
- Closed formulas and determinantal expressions for higher-order Bernoulli and Euler polynomials in terms of Stirling numbers
- A generalized series expansion of the arctangent function based on the enhanced midpoint integration
- A note on degenerate Bell numbers and polynomials