论文标题
切线和反线函数和Chebyshev多项式的较高衍生物
Higher Derivatives of the Tangent and Inverse Tangent Functions and Chebyshev Polynomials
论文作者
论文摘要
确定切线和双曲线切线功能的较高衍生物。陈述并证明了反向切线和反双曲线切线功能的较高衍生物的公式。证明了通过文献的另一个公式用于逆切线函数的较高衍生物，证明了第一和第二类的Chebyshev多项式的两个已知公式。从这些公式中，根据第二种的Chebyshev多项式，反切线和反双曲线切线函数的较高衍生物。
The higher derivatives of the tangent and hyperbolic tangent functions are determined. Formulas for the higher derivatives of the inverse tangent and inverse hyperbolic tangent functions as polynomials are stated and proved. Using another formula for the higher derivatives of the inverse tangent function from literature, two known formulas for the Chebyshev polynomials of the first and second kind are proved. From these formulas the higher derivatives of the inverse tangent and inverse hyperbolic tangent functions in terms of the Chebyshev polynomial of the second kind are provided.
