text: , the parameter Each of the above three quantities is completely determined by any of the others (given that they are non-negative). Thus, they can be used interchangeably.
  The other argument can likewise be expressed as , the amplitude, or as  or , where  and  is one of the Jacobian elliptic functions.
  Specifying the value of any one of these quantities determines the others. Note that  also depends on . Some additional relationships involving  include
  The latter is sometimes called the delta amplitude and written as . Sometimes the literature also refers to the complementary parameter, the complementary modulus, or the complementary modular angle. These are further defined in the article on quarter periods.
  In this notation, the use of a vertical bar as delimiter indicates that the argument following it is the "parameter" (as defined above), while the backslash indicates that it is the modular angle. The use of a semicolon implies that the argument preceding it is the sine of the amplitude:
  This potentially confusing use of different argument delimiters is traditional in elliptic integrals and much of the notation is compatible with that used in the reference book by Abramowitz and Stegun and that used in the integral tables by Gradshteyn and Ryzhik.