Is it possible to extend the Euler product analytically?

[tommy1729]

that solved the OP then.

but not my reply to it ...

i guess a nested solution is the only way :

find a function g(z) that converges for re > 1/2 only , find a product form f(z) for eta(z) that converges for re > a with a < 1/2.

then f(g(z)) is associated with the desired result.

now that i think of it , isnt there a product form known for eta(z) that works in the strip 0 < z < 2 ...

maybe there isnt a solution apart from the hadamard product form because log(eta(z)) is problematic because of the logaritmic riemann surface... (or leads us to hadamard anyway )

i guess the hadamard product form is the only solution for f(z) ??

i dont have time to consider this seriously at the moment ...

and it might not directly relate to tetration ... ( so sorry )

but i guess some are intrested in it anyway ?

or willing to help me

happy Xmas my fellow tetrationalists

tommy1729