There are still other conventions for the notation of elliptic integrals employed in the literature. The notation with interchanged arguments, , is often encountered; and similarly for the integral of the second kind. Abramowitz and Stegun substitute the integral of the first kind, , for the argument in their definition of the integrals of the second and third kinds, unless this argument is followed by a vertical bar: i.e. for . Moreover, their complete integrals employ the parameter as argument in place of the modulus , i.e. rather than . And the integral of the third kind defined by Gradshteyn and Ryzhik, , puts the amplitude first and not the "characteristic" .
There are still other conventions for the notation of elliptic integrals employed in the literature. The notation with interchanged arguments, , is often encountered; and similarly for the integral of the second kind Abramowitz and Stegun substitute the integral of the first kind, , for the argument in their definition of the integrals of the second and third kinds, unless this argument is followed by a vertical bar i.e. for . Moreover their complete integrals employ the parameter as argument in place of the modulus , i.e. rather than . And the integral of the third kind defined by Gradshteyn and Ryzhik, , puts the amplitude first and not the "characteristic" .