Modular Angle

Given a Modulus $k$ in an Elliptic Integral, the modular angle is defined by $k\equiv \sin \alpha$. An Elliptic Integral is written $I(\phi \vert m)$ when the Parameter is used, $I(\phi,k)$ when the Modulus is used, and $I(\phi \backslash \alpha)$ when the modular angle is used.

See also Amplitude, Characteristic (Elliptic Integral), Elliptic Integral, Modulus (Elliptic Integral), Nome, Parameter

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.