Lerch zeta function

In mathematics, the Lerch zeta function is a special function that generalizes the Hurwitz zeta function and the polylogarithm. It is given by

The Lerch zeta is related to the Lerch Transcendent, which is given by

by

Φ(exp(2πiλ),s,α) = L(λ,α,s)

The Hurwitz zeta function is a special case, given by

ζ(s,α) = L(0,α,s) = Φ(1,s,α)

The polylogarithm is a special case of the Lerch Zeta, given by

Li_s(x) = zΦ(z,s,1)

The Legendre chi function is a special case, given by

χ_n(z) = 2 ^{- n}zΦ(z²,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