li ⁡ ( x ) = γ + ln ⁡ ln ⁡ x + x ∑ n = 1 ∞ ( − 1 ) n − 1 ( ln ⁡ x ) n n ! 2 n − 1 ∑ k = 0 ⌊ ( n − 1 ) / 2 ⌋ 1 2 k + 1 . {\displaystyle \operatorname {li} (x)=\gamma +\ln \ln x+{\sqrt {x}}\sum _{n=1}^{\infty }{\frac {(-1)^{n-1}(\ln x)^{n}}{n!\,2^{n-1}}}\sum _{k=0}^{\lfloor (n-1)/2\rfloor }{\frac {1}{2k+1}}.}