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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 16, 2012 5:36 AM

On 4/16/12 9:52 AM, clicliclic@freenet.de wrote:
> I don't have much time, but to put an end to this Maplomatica insanity I
> have fired up Derive 6.10 and loaded my normative implementation of
> Lerch's transcendent. I find that
>
> lerch(z, 1, a) - lerch(1/z, 1, -a)
>
> numerically agrees with
>
> 1/a - (- 1/z)^a*pi/SIN(pi*(1 + a))
>
> everywhere except for real z with z> 1, and numerically agrees with
>
> 1/a + (-z)^(-a)*pi/SIN(pi*(1 - a))
>
> everywhere except for real z with 0< z< 1. Checked by plotting RE and
> IM versus z, versus z+#i, and versus z-#i for a = 1/2, and by plotting
> RE and IM versus a for z = 1/2 and for z = 2.
>
> Martin.

Thx. And MMA agrees with Derive.

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