On May 13, 2:50 am, kcrisman <[email protected]> wrote: > On May 12, 8:39 pm, Fredrik Johansson <[email protected]> > wrote: > > > On May 12, 11:19 pm, kcrisman <[email protected]> wrote: > > > > This should, in theory, give a plot of li(20^z) along the critical > > > line of the Riemann zeta function. Unfortunately, as you will see if > > > you plot this, it succeeds until it hits a branch cut (I assume), and > > > does not look so nice, not to mention missing the actual interesting > > > behavior. > > > You probably want ei(log(20)*z), not li(20^z). > > Bingo! Looks so beautiful. Thank you very much. > > Wikipedia says as much, of course, but just the equivalence. Is > there an easy explanation for why one seems to have this branch > phenomenon and the other doesn't?
Sure. li(z) is ei(log(z)) by definition. It's just a case of z*log(b) having simpler branch structure than log(b^z) (since b^z is a periodic function of z). Fredrik -- To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
