论文标题
关于不变函数的属性
On the properties of invariant functions
论文作者
论文摘要
如果$ f（x，y）$是满足$ y> 0 $和$ \ sum_ {r = 0}^{n-1} f（x+ry，ny）= f（x，y）$ for $ n = 1,2,3，\ ldots $的真实功能。许多特殊功能，包括Bernoulli多项式，伽马功能和Hurwitz Zeta功能与不变函数有关。在本文中，我们系统地研究了不变函数的属性。
If $f(x,y)$ is a real function satisfying $y>0$ and $\sum_{r=0}^{n-1}f(x+ry,ny)=f(x,y)$ for $n=1,2,3,\ldots$, we say that $f(x,y)$ is an invariant function. Many special functions including Bernoulli polynomials, Gamma function and Hurwitz zeta function are related to invariant functions. In this paper we systematically investigate the properties of invariant functions.
