Volume 9, Issue 3
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Elliptic Rational Functions
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Properties
We implemented 
in Mathematica as EllipticRationalFunction[n,
,x].
The main properties of 
follow.
- The squared function is even,
.- Over the unit interval
, 
is equiripple and 
.- For
, 
.
is monotonic increasing: 
, in the interval 
.- For
, 
.- The key feature of
is
- The poles of
can be simply expressed in terms of the zeros of 
:
The next figure illustrates the equiripple property of 
.
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