The following notation is a generalization of that of Khare and Sukhatme (2002).
Throughout this subsection and are positive integers with .
In the remainder of this section the rank of an identity is the largest number of elliptic function factors in any term of the identity. The value of determines the number of points in the identity. The argument is suppressed in the above notation, as all cyclic identities are independent of .
In this subsection and .
These identities are cyclic in the sense that each of the indices in the first product of, for example, the form are simultaneously permuted in the cyclic order: ; . Many of the identities that follow also have this property.
With defined as in (22.9.7),
Again with defined as in (22.9.7),