This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.1)


gives the Neville theta function .
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • NevilleThetaS is a meromorphic function of and has a complicated branch cut structure in the complex plane.
  • For certain special arguments, NevilleThetaS automatically evaluates to exact values.
Evaluate numerically:
Evaluate numerically:
Click for copyable input
Click for copyable input
Evaluate to high precision:
The precision of the output tracks the precision of the input:
NevilleThetaS threads element-wise over lists:
Evaluate for complex arguments and parameters:
NevilleThetaS evaluates symbolically for special arguments:
TraditionalForm formatting:
NevilleThetaS can be applied to power series:
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 the classical and arc length 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