(For other notation see Notation for the Special Functions.)
|the lattice parameter, .|
|the nome, , . Since is not a single-valued function of , it is assumed that is known, even when is specified. Most applications concern the rectangular case , , so that and and are uniquely related.|
|for (resolving issues of choice of branch).|
|set of all elements of , modulo elements of . Thus two elements of are equivalent if they are both in and their difference is in . (For an example see §20.12(ii).)|
The main functions treated in this chapter are the theta functions where and . When is fixed the notation is often abbreviated in the literature as , or even as simply , it being then understood that the argument is the primary variable. Sometimes the theta functions are called the Jacobian or classical theta functions to distinguish them from generalizations; compare Chapter 21.
Primes on the symbols indicate derivatives with respect to the argument of the function.
McKean and Moll’s notation: , . See McKean and Moll (1999, p. 125).
Additional notations that have been used in the literature are summarized in Whittaker and Watson (1927, p. 487).