(08/21/2016, 06:56 PM)Xorter Wrote: Hello, James! Hello, Everyone!
I am really interested in that how you could make that beautiful graph. Could you tell me, please?
Thank you very much.
Search for the cheta function on the forum and get its power series.
Take
\( f(t,x) = cheta(cheta^{-1}(x) + t) \)
define
\( x [t] y = f(t,f(-t,x) + f(-t,y))\,\,t<1 \)
\( x [t] y = f(t-1,yf(1-t,x))\,\,t \ge 1 \)
continuous solution which is analytic for t < 1 and t >1 with a singularity at t=1
oddly enough
\( x [t] e \) is analytic everywhere.