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Lerch zeta function
(Redirected from Lerch transcendant)
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
- Lis(x) = zΦ(z,s,1)
The Legendre chi function is a special case, given by
- χn(z) = 2 - nzΦ(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
Last updated: 05-27-2005 15:20:01
03-10-2013 05:06:04
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details