08/11/2013, 07:31 PM
Thanks for your quick reply.
Intresting idea.
Although I must say that - if I recall correct - the continuum sum does not imply uniqueness for tetration.
Then again you might not be after uniqueness but just a nice solution.
This is probably one of your best posts imho.
Although I havent checked all. It seems a bit weird , your integrals seem to lack a variable by being very selfreferential. This might not be a problem but it might be restrictive ... such as L-series or exponential sums ... maybe it can be solved by adding variables.
A problem might be that the n-th derivative is not just the formula of the nth integral with a minus sign added. I assume you knew that already from reading/lectures/exercises about fractional calculus.
Im curious about what others think of it.
regards
tommy1729
Intresting idea.
Although I must say that - if I recall correct - the continuum sum does not imply uniqueness for tetration.
Then again you might not be after uniqueness but just a nice solution.
This is probably one of your best posts imho.
Although I havent checked all. It seems a bit weird , your integrals seem to lack a variable by being very selfreferential. This might not be a problem but it might be restrictive ... such as L-series or exponential sums ... maybe it can be solved by adding variables.
A problem might be that the n-th derivative is not just the formula of the nth integral with a minus sign added. I assume you knew that already from reading/lectures/exercises about fractional calculus.
Im curious about what others think of it.
regards
tommy1729