The Riemann zeta function ζ(s) and the Hurwitz zeta function ζ(s, z) are built-in Derive functions (see Zeta FunctionsZeta_Functions).  The file ZetaFunctions.mth defines functions for approximating several functions related to the zeta function.  See the introduction to ExponentialIntegrals.mth7RN4D for a discussion of accuracy.  The function definitions in the file are automatically loaded when any of its functions are first used.


HURWITZ_ZETA(s, z, m) approximates to m+1 terms of a series for the Hurwitz or generalized zeta function ζ(s, z).  If the real part of s is greater than 1, ζ(s, z) is defined as Σ(1/(k+z)^s, k, 0, ∞); otherwise, it is defined by analytic extension over the rest of the complex plane.


POLYLOG(n, z, m) approximates to m terms of a series for the Jonquière polylogarithm function Lin(z) defined as the sum of z^k/k^n from k=1 to infinity.


LERCH_PHI(z, s, a, m) approximates to m terms of a series for the Lerch transcendent function Φ(z, s, a) defined as the sum of z^k/(a+k)^s from k=0 to infinity.


Other Utility File LibraryG5BS2R 

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