On the properties of invariant functions

2022/09/29 by Sun, Zhi-Hong · 1 citation
#26A45 #33B10 #33B15 #33E99 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Primary 26B99 #Secondary 11B68

paper · doi:10.48550/arxiv.2209.14625

Abstract

If f(x,y) is a real function satisfying y>0 and ∑_r=0^n-1f(x+ry,ny)=f(x,y) for n=1,2,3,…, 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.

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