Built-in Mathematica Symbol

NevilleThetaC

NevilleThetaC[z, m]
gives the Neville theta function

.

NevilleThetaC[z, m] is a meromorphic function of and has a complicated branch cut structure in the complex -plane.

For certain special arguments, NevilleThetaC automatically evaluates to exact values.

Evaluate numerically:

Series expansion:

Evaluate numerically:

Series expansion:

Evaluate to high precision:

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

NevilleThetaC threads element-wise over lists:

Evaluate for complex arguments and parameters:

NevilleThetaC evaluates symbolically for special arguments and parameters:

NevilleThetaC can be applied to a power series:

Plot over the

plane:

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:

Numerically find a root of a transcendental equation:

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