# 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} }

- Published in Applied Mathematics and Computation 2015
DOI:10.1016/j.amc.2015.02.027

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.

#### Topics from this paper.

#### Citations

##### Publications citing this paper.

SHOWING 1-10 OF 23 CITATIONS

## On complete monotonicity for several classes of functions related to ratios of gamma functions

VIEW 1 EXCERPT

CITES BACKGROUND

## Higher derivatives of the inverse tangent function and a summation formula involving binomial coefficients.

VIEW 2 EXCERPTS

CITES BACKGROUND

## Realization of a Method for Calculating Bell Polynomials Based on Compositae of Generating Functions

VIEW 2 EXCERPTS

CITES BACKGROUND & METHODS

## SPECIAL VALUES OF THE BELL POLYNOMIALS OF THE SECOND KIND FOR SOME SEQUENCES AND FUNCTIONS

VIEW 1 EXCERPT

CITES BACKGROUND

## Some recurrence formulas for the Hermite polynomials and their squares

VIEW 1 EXCERPT

CITES METHODS

## An explicit formula for derivative polynomials of the tangent function

VIEW 1 EXCERPT

CITES BACKGROUND

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 18 REFERENCES

## Advanced Combinatorics The Art Of Finite And Infinite Expansions

VIEW 7 EXCERPTS

HIGHLY INFLUENTIAL

## The higher derivatives of the inverse tangent function and rapidly convergent BBP-type formulas for pi.

VIEW 7 EXCERPTS

HIGHLY INFLUENTIAL