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

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 did Posts: 80 Registered: 9/14/05
Re: Inversion Lerch Phi
Posted: Apr 13, 2012 5:11 PM
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On 4/13/12 10:48 PM, Axel Vogt wrote:
> I do not yet agree (for the versions: I used Maple 16):
>
> MMA just has the the problem to numerical evaluate the example, e.
> And I do not want to assume that MMA is right.
>
> And the final example f2 - e is just a reformulation of that for e:
> since f2 will be 0 it reduces to that.
>
> Would you mind to check MMA 7 with z = 2 - 1e-1000 * I?

Without sufficient precision, MMA will "see" this z on the branch cut:

z = 2 - I*10^(-1000); a = 1/2;
Block[{\$MaxExtraPrecision = 100},
N[ HurwitzLerchPhi[1/z, 1, -a] - HurwitzLerchPhi[z, 1, a] +
1/a - (-1/z)^a*Pi/Sin[Pi*(1 + a)] , 100]]

0.*10^-100 +
4.4428829381583662470158809900606936986146216893756902230853956069564\
34793099473910575326934764765237 I

But with enough digits, it "sees" it's not on the branch and your
formula appears correct:

z = 2 - I*10^(-1000); a = 1/2;
Block[{\$MaxExtraPrecision = 1100},
N[ HurwitzLerchPhi[1/z, 1, -a] - HurwitzLerchPhi[z, 1, a] +
1/a - (-1/z)^a*Pi/Sin[Pi*(1 + a)] , 1100]]

0.*10^-2199 + 0.*10^-2199 I

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

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