Built-in Mathematica Symbol

NevilleThetaD

NevilleThetaD[z, m]
gives the Neville theta function

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MORE INFORMATION

Mathematical function, suitable for both symbolic and numerical manipulation.

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NevilleThetaD[z, m] 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.

NevilleThetaD can be evaluated to arbitrary numerical precision.

NevilleThetaD automatically threads over lists.

EXAMPLES

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Basic Examples (2)

Evaluate numerically:

Scope (5)

Evaluate to high precision:

The precision of the output tracks the precision of the input:

NevilleThetaD threads element-wise over lists:

Evaluate for complex arguments and parameters:

NevilleThetaD evaluates symbolically for special arguments:

TraditionalForm formatting:

Generalizations & Extensions (1)

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

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Plot the curve for real u:

Verify that points on the curve satisfy

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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:

Properties & Relations (3)

Basic simplifications are automatically carried out:

Use FullSimplify for expressions containing Neville theta functions:

Numerically find a root of a transcendental equation:

Possible Issues (1)

Machine-precision input is insufficient to give a correct answer: