LerchPhiClassical[z, s, a] \[Proportional] Sum[(z^k (1 + O[a - Subscript[a, 0]]))/ (E^(2 I Pi s Floor[(-(1/(2 Pi))) (Arg[(a + k)/(Subscript[a, 0] + k)] + Arg[-Subscript[a, 0] - k])]) (Subscript[a, 0] + k)^s), {k, 0, n - 1}] + (z^n/(Subscript[a, 0] + n)^s + z^(n + 1) LerchPhiClassical[z, s, Subscript[a, 0] + n + 1]) (1 + O[a - Subscript[a, 0]]) /; -n < Subscript[a, 0] < -n + 1 && Element[n, Integers] && n > 0

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2007-05-02