where , .
The left-hand sides of (20.5.10) and (20.5.11) are replaced
by their limiting values when or are undefined.
With the given conditions the infinite series in
(20.5.10)–(20.5.13) converge absolutely and uniformly
in compact sets in the -plane.
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)).