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

# NevilleThetaN

 NevilleThetaNgives the Neville theta function .
• Mathematical function, suitable for both symbolic and numerical manipulation.
• NevilleThetaN is a meromorphic function of and has a complicated branch cut structure in the complex plane.
• For certain special arguments, NevilleThetaN automatically evaluates to exact values.
Evaluate numerically:
Evaluate numerically:
 Out[1]=

 Out[1]=
 Scope   (5)
Evaluate to high precision:
The precision of the output tracks the precision of the input:
Evaluate for complex arguments and parameters:
NevilleThetaN evaluates symbolically for special arguments:
NevilleThetaN can be applied to power series:
 Applications   (5)
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 :
Current flow in a rectangular conducting sheet with voltage applied at a pair of opposite corners:
Plot the flow lines:
Parametrize a lemniscate by arc length:
Show arc length and classical parametrizations:
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:
New in 3