BUILT-IN MATHEMATICA SYMBOL

EllipticThetaPrime

gives the derivative with respect to u of the theta function

.

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

Evaluate numerically:

Series expansion:

Evaluate numerically:

Out[1]=

Out[1]=

Series expansion:

Out[1]=

Evaluate numerically for complex arguments:

Evaluate to high precision:

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

EllipticThetaPrime threads element-wise over lists:

EllipticThetaPrime evaluates symbolically for special arguments:

EllipticThetaPrime can be applied to power series:

Solution of the 1D heat equation with Dirichlet boundary condition and initial condition

:

Calculate the temperature gradient:

Plot the temperature gradient:

Electrostatic force in a NaCl-like crystal with point-like ions:

Plot the magnitude of the force in a plane through the crystal:

The canonical rotational distribution function for linear molecules

:

Plot a numerical approximation of the partition function:

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

Use arbitrary-precision arithmetic to obtain the correct result:

The first argument must be an explicit integer between 1 and 4:

Different argument conventions exist:

Visualize a function with a boundary of analyticity: