关于非常值周期函数的超越性

On the Transcendency of Non-constant Periodic Functions

摘要

摘要:两个定理:Ⅰ)如y=f(x)是超越的，则其反函数（如存在）也是；Ⅱ)任何非常值周期函数是超越的，被证明了.借助于它们,建立起圆函数、指数函数及它们的反函数的超越性,并指出一些“奇异”的函数,如Dirichlet函数及Kronecker delta符号的超越性.

Abstract:Two theorems: I. if y=f(x) is transcendental, so does its inverse; and II. any periodic function, not being a constant, is transcendental, are proved. By means of them, the transcendency of the circular function, exponential function and their inverses are established. Apart from these, such functions as Dirichlet function and kronecker delta symbol are pointed out to be transcendental.