The inverse Jacobian elliptic functions can be defined in an analogous manner to the inverse trigonometric functions (§4.23). With real variables, the solutions of the equations
are denoted respectively by
Each of these inverse functions is multivalued. The principal values satisfy
can be transformed into normal form by elementary change of variables. Comprehensive treatments are given by Carlson (2005), Lawden (1989, pp. 52–55), Bowman (1953, Chapter IX), and Erdélyi et al. (1953b, pp. 296–301). See also Abramowitz and Stegun (1964, p. 596).