Lerch Zeta Function

$L(\backslash lambda,\; \backslash alpha,\; s)\; =\; \backslash sum\_\{n=0\}^\backslash infty$

$\backslash Phi(z,\; s,\; \backslash alpha)\; =\; \backslash sum\_\{n=0\}^\backslash infty$

$\backslash Phi(\backslash exp\; (2\backslash pi\; i\backslash lambda),\; s,\backslash alpha)=L(\backslash lambda,\; \backslash alpha,s)$

$\backslash zeta(s,\backslash alpha)=L(0,\; \backslash alpha,s)=\backslash Phi(1,s,\backslash alpha)$

$\backslash textrm\{Li\}\_s(x)=z\backslash Phi(z,s,1)$

$\backslash chi\_n(z)=2^\{-n\}z\; \backslash Phi\; (z^2,n,1/2)$

External links

• Ramunas Garunkstis, Approximation of the Lerch Zeta Function (PDF)
• Sergej V. Aksenov and Ulrich D. Jentschura, C and Mathematica Programs for Calculation of Lerch's Transcendent

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