Amplitude

The variable $\phi$ used in Elliptic Functions and Elliptic Integrals, which can be defined by

$$\phi=\mathop{\rm am}\nolimits u\equiv \int \mathop{\rm dn}\nolimits u\,du,$$

where $\mathop{\rm dn}\nolimits (u)$ is a Jacobi Elliptic Function. The term ``amplitude'' is also used to refer to the maximum offset of a function from its baseline level.

See also Argument (Elliptic Integral), Characteristic (Elliptic Integral), Delta Amplitude, Elliptic Function, Elliptic Integral, Jacobi Elliptic Functions, Modular Angle, 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.

Fischer, G. (Ed.). Plate 132 in Mathematische Modelle/Mathematical Models, Bildband/Photograph Volume. Braunschweig, Germany: Vieweg, p. 129, 1986.