自然指数函数展开式的多重分割法（三）──抽象双曲函数

The Method of Many Seperable Expansions for the Expansion of Exponential Function(Ⅲ)──The Abstract Hyperbolic Function

对于形式幂级数Ａ（ｔ）施行ｍ重分割法得出形式幂级数Ｂ１（ｔ），Ｂ２（ｔ），…，Ｂｍ（ｔ）称为抽象双曲函数．本文主要探讨Ａ（ｔ）与Ｂ１（ｔ），Ｂ２（ｔ），…，Ｂｍ（ｔ）之间的表达式、行列式性质及其应用（如Ｗａｒｉｎｇ公式的推广等）．

Applying the method of m-seperable expansions to the formal power series A(t)we have got the formal power series B1(t),B2(t),…,Bn(t) which are called abstract hyperbolic functon. In this paper we study the expression among B1(t),B2(t),…,Bn(t)and A(t).We also reveal the property of the determinant and its application (for example,the generalization of Waring's formula).