02/03/2008, 08:48 PM

Is it possible to have analytic values y = b[s]x for x -> -oo, [s] odd integer in any of the bases?

Put other way, do there ( does there) exist a base ( an algorithm to construct a base) which would lead to analytic values for all odd [s] as x-> - oo?

I have a gut feeling this relates to Euler's old problem of finding sum of alternating sign terms of :

1/1^n -1/2^n+1/3^n-1/4^n+1/5^n-1/6^n+1/7^n - where n- odd integer.

Well , Euler new only one hyperoperation-tetration, so he could not go above n=3 in his search.

Or, may be this sum is already found?

Ivars

Put other way, do there ( does there) exist a base ( an algorithm to construct a base) which would lead to analytic values for all odd [s] as x-> - oo?

I have a gut feeling this relates to Euler's old problem of finding sum of alternating sign terms of :

1/1^n -1/2^n+1/3^n-1/4^n+1/5^n-1/6^n+1/7^n - where n- odd integer.

Well , Euler new only one hyperoperation-tetration, so he could not go above n=3 in his search.

Or, may be this sum is already found?

Ivars