Zeta function for Complex Sqrt[+1]
- To: mathgroup at smc.vnet.net
- Subject: [mg41434] Zeta function for Complex Sqrt[+1]
- From: "Edward Jones" <e.mjones at btopenworld.com>
- Date: Mon, 19 May 2003 05:14:00 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
zetaeuler[] evaluates the zeta function by Eulers transformation
of series. It can be checked against the Mathematica Zeta[].
Greater accuracy is achieved by increasing terms and extraterms.
zetaeulerij[] evaluates numerically the zeta function for complex
values involving ij where ij=Complex Sqrt[+1].
zetaeulerij[x+y*ij] appears to be a regular function, unlike
Zeta[x+I*y] with Abs[zetaeulerij[x+y*ij]] increasing in an
exponential fashion with y. You can Plot using eg:
Plot3D[Abs[zetaeulerij[x+ij*y]/.ij->I],{x},{y}].
Can anyone develop this topic?
Edward Jones.