## Parameter

A parameter used in Elliptic Integrals defined to be , where is the Modulus. An Elliptic Integral is written when the parameter is used. The complementary parameter is defined by

 (1)

where is the parameter. Let be the Nome, the Modulus, and the Parameter. Then
 (2)

where is the complete Elliptic Integral of the First Kind. Then the inverse of is given by
 (3)

where is a Theta Function.

See also Amplitude, Characteristic (Elliptic Integral), Elliptic Integral, Elliptic Integral of the First Kind, Modular Angle, Modulus (Elliptic Integral), Nome, Parameter, Theta Function

References

Abramowitz, M. and Stegun, C. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 590, 1972.