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Topic: Inversion Lerch Phi
Replies: 38   Last Post: May 27, 2012 2:36 PM

 Messages: [ Previous | Next ]
 did Posts: 80 Registered: 9/14/05
Re: Inversion Lerch Phi
Posted: Apr 14, 2012 1:38 PM

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

Date Subject Author
4/12/12 did
4/12/12 clicliclic@freenet.de
4/12/12 did
4/19/12 clicliclic@freenet.de
4/26/12 clicliclic@freenet.de
4/26/12 clicliclic@freenet.de
4/26/12 clicliclic@freenet.de
4/26/12 did
4/27/12 clicliclic@freenet.de
5/4/12 clicliclic@freenet.de
5/5/12 did
5/5/12 clicliclic@freenet.de
5/27/12 clicliclic@freenet.de
5/27/12 Axel Vogt
4/13/12 clicliclic@freenet.de
4/13/12 Axel Vogt
4/13/12 did
4/13/12 Axel Vogt
4/13/12 did
4/13/12 did
4/13/12 Axel Vogt
4/13/12 Axel Vogt
4/13/12 did
4/13/12 Axel Vogt
4/13/12 did
4/13/12 Axel Vogt
4/14/12 clicliclic@freenet.de
4/14/12 did
4/14/12 did
4/15/12 clicliclic@freenet.de
4/15/12 did
4/15/12 Axel Vogt
4/15/12 did
4/15/12 Axel Vogt
4/16/12 clicliclic@freenet.de
4/16/12 did
4/14/12 Axel Vogt
4/13/12 Axel Vogt
4/16/12 Joe keane