# EllipticExpPrime

EllipticExpPrime[u,{a,b}]

gives the derivative of EllipticExp[u,{a,b}] with respect to u.

# Details • Mathematical function, suitable for both symbolic and numerical manipulation.
• For certain special arguments, EllipticExpPrime automatically evaluates to exact values.
• EllipticExpPrime can be evaluated to arbitrary numerical precision.

# Examples

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## Basic Examples(2)

Evaluate numerically:

Plot the components of EllipticExpPrime over several real periods:

## Scope(9)

### Numerical Evaluation(4)

Evaluate numerically:

Evaluate to high precision:

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

Complex number inputs:

Evaluate efficiently at high precision:

### Specific Values(2)

Values at fixed points:

Value at zero:

### Visualization(2)

Plot the EllipticExpPrime function for various parameters:

Plot the real part of :

Plot the imaginary part of :

### Integration(1)

Compute the indefinite integral using Integrate:

Verify the anti-derivative:

## Applications(1)

Visualize the function:

## Properties & Relations(4)

EllipticExpPrime is the derivative of EllipticExp:

EllipticExpPrime is closely related to the WeierstrassP function and its derivative:

Compare numerical values:

Evaluate the elliptic exponential and its derivative:

EllipticExpPrime can be expressed in terms of the components of EllipticExp:

WeierstrassHalfPeriods can be used to compute the two linearly independent periods of EllipticExpPrime:

Compare numerical evaluations of EllipticExpPrime at congruent points in the complex plane: