# §23.10 Addition Theorems and Other Identities

###### Contents

23.10.1
23.10.2
23.10.3

For further addition-type identities for the -function see Lawden (1989, §6.4).

If , then

23.10.5

and

## §23.10(ii) Duplication Formulas

23.10.7

(23.10.8) continues to hold when , , are permuted cyclically.

23.10.9

## §23.10(iv) Homogeneity

For any nonzero real or complex constant

23.10.17
23.10.18
23.10.19

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).