A triply periodic function is a function having three distinct periods. Jacobi (1835) proved that a single-valued univariate function cannot have more than two distinct periods (Boyer and Merzbach 1991, p. 525), thus showing that elliptic functions are the most general multiply periodic single-valued functions possible in a single variable.
Triply Periodic Function
See also
Doubly Periodic Function, Elliptic Function, Periodic Function, Singly Periodic FunctionExplore with Wolfram|Alpha
References
Boyer, C. B. and Merzbach, U. C. A History of Mathematics, 2nd ed. New York: Wiley, 1991.Jacobi, C. G. J. J. für Math. 13, 55-56, 1835. Reprinted in Gesammelte Werke, Vol. 2, 2nd ed. Providence, RI: Amer. Math. Soc., pp. 25-26, 1969.Referenced on Wolfram|Alpha
Triply Periodic FunctionCite this as:
Weisstein, Eric W. "Triply Periodic Function." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TriplyPeriodicFunction.html