カテゴリー: 多重対数関数

\[ \int z^{\alpha}\Li_{n}\left(z\right)dz=\frac{\left(-1\right)^{n}z^{\alpha+1}}{\left(\alpha+1\right)^{n}}\left\{ \sum_{k=1}^{n}\left(\left(-1\right)^{k}\left(\alpha+1\right)^{k-1}\Li_{k}\left(z\right)\right)+\frac{z}{\alpha+2}F\left(1,\alpha+2;\alpha+3;z\right)\right\} \]

\[ Li_{s+1}'(z)=\frac{Li_{s}(z)}{z} \]

\[ \Li_{1}(z)=-\log(1-z) \]

\[ Li_{s}(z)=\sum_{k=1}^{\infty}\frac{z^{k}}{k^{s}} \]