§20.5 Infinite Products and Related Results

where , .

§20.5(ii) Logarithmic Derivatives

When ,

20.5.11

The left-hand sides of (20.5.10) and (20.5.11) are replaced by their limiting values when or are undefined.

When ,

20.5.12
20.5.13

With the given conditions the infinite series in (20.5.10)–(20.5.13) converge absolutely and uniformly in compact sets in the -plane.

§20.5(iii) Double Products

These double products are not absolutely convergent; hence the order of the limits is important. The order shown is in accordance with the Eisenstein convention (Walker (1996, §0.3)).