I corrected the mistakes of taking logarithms from h(z) in previous posts.

But one could still ask if there exists transformation H such that :

Then

would always be a divergent sum, related to h(z). Instead of all z being similar, one can have e.g z=2^n or other general term, then these sums will coincide with usually known divergent sums like 1+2+4+8+16+32........ or 1+1+1+1+1+1....

Similarly 1/h(z) could be transformed in z/z/z/z/z/z/z.......... and sums would be -z-z-z-z-z-z-...?

Ivars

But one could still ask if there exists transformation H such that :

Then

would always be a divergent sum, related to h(z). Instead of all z being similar, one can have e.g z=2^n or other general term, then these sums will coincide with usually known divergent sums like 1+2+4+8+16+32........ or 1+1+1+1+1+1....

Similarly 1/h(z) could be transformed in z/z/z/z/z/z/z.......... and sums would be -z-z-z-z-z-z-...?

Ivars