For further addition-type identities for the -function see
Lawden (1989, §6.4).
If , then
(23.10.8) continues to hold when , , are
For any nonzero real or complex constant
Also, when is replaced by the lattice invariants
and are divided by and , respectively.
For these results and further identities see Lawden (1989, §6.6) and
Apostol (1990, p. 14).