EllipticExpPrime

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.

open allclose all

Evaluate numerically:

Plot the components of EllipticExpPrime over several real periods:

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:

Values at fixed points:

Value at zero:

Plot the EllipticExpPrime function for various parameters:

Plot the real part of :

Plot the imaginary part of :

Compute the indefinite integral using Integrate:

Verify the anti-derivative:

Visualize the function:

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:

Top