(For other notation see Notation for the Special Functions.)
|modulus. Except in §§22.3(iv), 22.17, and 22.19, .|
|complementary modulus, . If , then .|
|,||, (complete elliptic integrals of the first kind (§19.2(ii))).|
|nome. except in §22.17; see also §20.1.|
All derivatives are denoted by differentials, not primes.
The functions treated in this chapter are the three principal Jacobian elliptic functions , , ; the nine subsidiary Jacobian elliptic functions , , , , , , , , ; the amplitude function ; Jacobi’s epsilon and zeta functions and .