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Date: 25-8-2019
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Date: 21-5-2019
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Date: 26-9-2019
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The elliptic exponential function gives the value of
in the elliptic logarithm
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for and
real such that
.
It is implemented in the Wolfram Language 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.
REFERENCES:
Wolfram, S. The Mathematica Book, 5th ed. Champaign, IL: Wolfram Media, p. 788, 2003.
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