Taylor series of cheta

[Xorter]

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.

How can it help me to evaluate 3[0.5]3 and 3[1.5]3?