11/01/2010, 08:32 PM

Hi.

Does this lead anywhere, or does it just fail?

Take the partial sums of , a function called the "exponential sum function":

.

If we take this at odd values of , there will be a real fixed point. Take the regular iteration at this real fixed point, shifted so that it equals 1 at 0, call it , that is, regular iteration developed at the real fixed point, iterating "1" (i.e. offset so it equals 1 at 0). Now, what does

do?

Does this lead anywhere, or does it just fail?

Take the partial sums of , a function called the "exponential sum function":

.

If we take this at odd values of , there will be a real fixed point. Take the regular iteration at this real fixed point, shifted so that it equals 1 at 0, call it , that is, regular iteration developed at the real fixed point, iterating "1" (i.e. offset so it equals 1 at 0). Now, what does

do?