did
Posts:
73
Registered:
9/14/05
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Re: Inversion Lerch Phi
Posted:
Apr 14, 2012 1:38 PM
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On 4/14/12 7:32 PM, Did wrote:
> polylog(s,z) + (-1)^s*polylog(s,1/z) =
> (2*I*Pi)^nu/GAMMA(s)*Zeta(0,1-s,log(z)/I/2/Pi) -
> Heaviside(-argument(z-1))*I*2*Pi*(log(z))^(s-1)/GAMMA(s)
Should have been:
polylog(s,z) + (-1)^s*polylog(s,1/z) =
> (2*I*Pi)^s/GAMMA(s)*Zeta(0,1-s,log(z)/I/2/Pi) -
> Heaviside(-argument(z-1))*I*2*Pi*(log(z))^(s-1)/GAMMA(s)
> f(z) = Principal Value of Integral of [ Phi(exp(I*(z-u)),s,a) -
> Phi(1/exp(I*(z-u)),s,-a) ] g(u) du
Should have been:
f(z) = Principal Value of Integral of [ Phi(exp(I*(z-u)),s,a) + (-1)^s
* Phi(1/exp(I*(z-u)),s,-a) ] g(u) du
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