This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

 NevilleThetaDgives the Neville theta function .
• Mathematical function, suitable for both symbolic and numerical manipulation.
• NevilleThetaD is a meromorphic function of and has a complicated branch cut structure in the complex plane.
• For certain special arguments, NevilleThetaD automatically evaluates to exact values.
Evaluate numerically:
Evaluate numerically:
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 Scope   (5)
Evaluate to high precision:
The precision of the output tracks the precision of the input:
Evaluate for complex arguments and parameters:
NevilleThetaD evaluates symbolically for special arguments:
NevilleThetaD can be applied to power series:
 Applications   (7)
Plot over the arguments' plane:
Conformal map from a unit triangle to the unit disk:
Show points before and after the map:
Uniformization of a Fermat cubic :
Plot the curve for real :
Verify that points on the curve satisfy :
Parametrize a lemniscate by arc length:
Show the classical and arc length parametrizations:
Complex parametrization of a sphere:
The square of all points on the complex sphere is 1:
Conformal map from an ellipse to the unit disk:
Visualize the map:
Cartesian coordinates of a pendulum:
Plot the time dependence of the coordinates:
Plot the trajectory:
Basic simplifications are automatically carried out:
Use FullSimplify for expressions containing Neville theta functions:
Numerically find a root of a transcendental equation:
Machine-precision input is insufficient to give a correct answer:
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