${\displaystyle s\in (1,\infty )}$

${\displaystyle k\in \{1,2,\dots \}}$

${\displaystyle {\frac {1/k^{s}}{\zeta (s)}}}$

${\displaystyle {\frac {H_{k,s}}{\zeta (s)}}}$

${\displaystyle {\frac {\zeta (s-1)}{\zeta (s)}}~{\textrm {dla}}~s>2}$
gdzie ζ(s) to funkcja dzeta Riemanna

${\displaystyle 1}$

${\displaystyle {\frac {\zeta (s)\zeta (s-2)-\zeta (s-1)^{2}}{\zeta (s)^{2}}}~{\textrm {dla}}~s>3}$

${\displaystyle \sum _{k=1}^{\infty }{\frac {1/k^{s}}{\zeta (s)}}\log(k^{s}\zeta (s))}$

${\displaystyle {\frac {\operatorname {Li} _{s}(e^{t})}{\zeta (s)}}}$

${\displaystyle {\frac {\operatorname {Li} _{s}(e^{it})}{\zeta (s)}}}$