初值解在复变函数公式证明中的应用

Applying the differential equation,s problem of initial value to the proof of hyperbolic functions of the complex variable formula

通过对复数域上二阶常系数线形齐次微分方程初值问题的求解,给出了复变双曲函数若干公式的一种新的证明方法。体现了微分方程与复变函数论的两个学科之间的密切关系,也体现了微分方程理论在解决其他数学分支问题中的重要作用。

Inthis paper we offer a new method to prove formulae of hyperbolc function of the complex variable by solving initial value problem of homogeneous linear equating of the second order with constant coefficients. It show the confidential relations between differential equation and function of a complex variable, also show the differential equation, s important effect in solving problem of other mathematical branches.