Abstract:Let p,x be real numbers, and s be a complex number, with ℜ(s)>1−r, p≥1, and x+1>0. The zeta function Zpα(s;x) is defined by Zpα(s;x)=1Γ(s)∫0∞e−xtet−1Liα1−e−tpts−1dt, where α=(α1,…,αr) is a r-tuple pos...Let p,x be real numbers, and s be a complex number, with ℜ(s)>1−r, p≥1, and x+1>0. The zeta function Zpα(s;x) is defined by Zpα(s;x)=1Γ(s)∫0∞e−xtet−1Liα1−e−tpts−1dt, where α=(α1,…,αr) is a r-tuple positive integers, and Liα(z) is the one-variable multiple polylogarithms. Since Z1α(s;0)=ξ(α;s), we call this function as a generalized Arakawa-Kaneko zeta function. In this paper, we investigate the properties and values of Zpα(s;x) with different values s, x, and p. We then give some applications on them.Read More