【摘要】 本文提出两类新的高级超越函数──Ｓ＋－函数和Ｓ－－函数，总称为Ｓ－函数． 指数函数、正弦函数、余弦函数、双曲正弦、双曲余弦、ｎ阶三角函数和ｎ阶双曲 函数等．都是Ｓ－函数的特殊形式．文中证明了关于Ｓ－函数及其各阶导数的性质 的三个定理．列举出Ｓ－函数的一些公式，获得了各类ｎ阶广义阻尼振动方程的通 解，这些通解都由Ｓ－函数完全表达．更多还原

【Abstract】 In this article, two sorts of new higher transcendental functions-S+-fun-ction and S-function are established. The total of these two sorts of functions is called S-functions The indicial function, sinusoidal function, cosinusoidal function, hyperbolic sinusoidal function, hyperbolic cosinusoidal function, trigonometric function of n-order and hyperbolic function of n-order etch are all belong to S-functions. Three theorems about properties of S-functions and of each order of their derivatives are proved. Many formulae about S-functions are listed, Finally, we obtain the general solution of every kind of general damping oscillating equations of n-order. These general solutions can wholly be expressed with S-functions.更多还原