The elliptic exponential function gives the value of in the elliptic logarithm

for and real such that .

It is implemented in Mathematica as EllipticExp[u, a, b], which returns together with the superfluous parameter which multiplies the above integral by a factor of .

The top plot above shows (red), (violet), and (blue) for . The other plots show in the complex plane.

The plots above show in the complex plane for .

As can be seen from the plots, the elliptic exponential function is doubly periodic in the complex plane.

RELATED WOLFRAM SITES: http://functions.wolfram.com/EllipticFunctions/EllipticExp/, http://functions.wolfram.com/EllipticFunctions/EllipticExpPrime/

Wolfram, S. The Mathematica Book, 5th ed. Champaign, IL: Wolfram Media, p. 788, 2003.

CITE THIS AS:

Weisstein, Eric W. "Elliptic Exponential Function." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/EllipticExponentialFunction.html