(02/10/2011, 05:59 AM)sheldonison Wrote:(02/10/2011, 04:20 AM)mike3 Wrote: ....What is the decremented exponential? I'm guessing here, (I apologize for sometimes having trouble seeing the big picture behind the equations), but are these coefficients related to the superfunction of f(z)=exp(z)-1?
Letting \( r_{n, m} = \frac{u^{n-1}}{1 - u^{n-1}} \frac{m!}{n!} \left{{n \atop m}\right} \), we now have \( \chi_n = a_n \), thus an explicit, non-recursive formula for the coefficients of the regular Schroder function of the decremented exponential.
-Sheldon
Earlier here, I mention finding the regular Schroder function of the function \( e^{uz} - 1 \), about the fixed point of \( z = 0 \) of course. That function is the decremented exponential.
