Explicit expressions for a family of the Bell polynomials and applications

@article{Qi2015ExplicitEF,
  title={Explicit expressions for a family of the Bell polynomials and applications},
  author={Feng Qi and Miao-Miao Zheng},
  journal={Applied Mathematics and Computation},
  year={2015},
  volume={258},
  pages={597-607}
}
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 the Bell polynomials of the second kind related to the square function, and finally apply these explicit expressions to find explicit formulas for derivatives of some elementary functions. 

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