(08/13/2011, 10:32 AM)sheldonison Wrote: Henryk, Do you have a reference for showing that the base change function is infinitely differentiable? Perhaps Walker's paper?

There are two papers I know of:

Viana da Silva, M. (1988). The differentiability of the hairs of exp(Z). Proc. Am. Math. Soc., 103(4), 1179–1184.

Walker, P. L. (1991). Infinitely differentiable generalized logarithmic and exponential functions. Math. Comput., 57(196), 723–733.

I send them via e-mail to you.