# 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 EllipticExpPrime[z,{1,2}]:

Plot the imaginary part of EllipticExpPrime[z,{1,2}]:

### 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:

Wolfram Research (1991), EllipticExpPrime, Wolfram Language function, https://reference.wolfram.com/language/ref/EllipticExpPrime.html.

#### Text

Wolfram Research (1991), EllipticExpPrime, Wolfram Language function, https://reference.wolfram.com/language/ref/EllipticExpPrime.html.

#### CMS

Wolfram Language. 1991. "EllipticExpPrime." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/EllipticExpPrime.html.

#### APA

Wolfram Language. (1991). EllipticExpPrime. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/EllipticExpPrime.html

#### BibTeX

@misc{reference.wolfram_2024_ellipticexpprime, author="Wolfram Research", title="{EllipticExpPrime}", year="1991", howpublished="\url{https://reference.wolfram.com/language/ref/EllipticExpPrime.html}", note=[Accessed: 23-April-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_ellipticexpprime, organization={Wolfram Research}, title={EllipticExpPrime}, year={1991}, url={https://reference.wolfram.com/language/ref/EllipticExpPrime.html}, note=[Accessed: 23-April-2024 ]}