growth of a function

Jarle

Does there exist a continuous function which outgrows polynomial growth, but not exponential growth?

I.e. does a there exist a continuous function f such that and for all positive real n and a?

hamster143

Yes. Look at it this way: you take logs of the polynomial and the exponential, you get and . Can you find a function that grows faster than g_1 and slower than g_2 for all C? Clearly you can, because ln grows extremely slowly.

Jarle

Thanks,

is such a function.

hamster143

Or , or .

Jarle

I'm sure we can find many as you pointed out.