DLMF:25.12.E12 (Q7731): Difference between revisions

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| ln z | < 2 π 𝑧 2 𝜋 {\displaystyle{\displaystyle|\ln z|<2\pi}}

|\ln@@{z}|<2\pi
Property / constraint: | ln z | < 2 π 𝑧 2 𝜋 {\displaystyle{\displaystyle|\ln z|<2\pi}} / rank
 
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Revision as of 18:18, 30 December 2019

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DLMF:25.12.E12
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    Li s ( z ) = Γ ( 1 - s ) ( ln 1 z ) s - 1 + n = 0 ζ ( s - n ) ( ln z ) n n ! , polylogarithm 𝑠 𝑧 Euler-Gamma 1 𝑠 superscript 1 𝑧 𝑠 1 superscript subscript 𝑛 0 Riemann-zeta 𝑠 𝑛 superscript 𝑧 𝑛 𝑛 {\displaystyle{\displaystyle\mathrm{Li}_{s}\left(z\right)=\Gamma\left(1-s% \right)\left(\ln\frac{1}{z}\right)^{s-1}+\sum_{n=0}^{\infty}\zeta\left(s-n% \right)\frac{(\ln z)^{n}}{n!},}}
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    DLMF:25.12.E12
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    | ln z | < 2 π 𝑧 2 𝜋 {\displaystyle{\displaystyle|\ln z|<2\pi}}
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