EllipticF

Evaluate for complex arguments:

Evaluate to high precision:

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

Simple exact values are generated automatically:

EllipticF threads element-wise over lists:

Expand in series with respect to the modulus:

TraditionalForm formatting:

EllipticF can be applied to power series:

Carry out an elliptic integral:

Plot an incomplete elliptic integral over the complex plane:

Calculate the surface area of a triaxial ellipsoid:

The area of an ellipsoid with half axes 3, 2, 1:

Calculate volume through integrating the differential surface elements:

Arc length parametrization of a curve that minimizes the integral of the square of its curvature:

Parametrization of a mylar balloon (two flat sheets of plastic sewn together at their circumference and then inflated):

Plot the resulting balloon:

Calculate the ratio of the main curvatures:

Express the radius of the original sheets through the radius of the inflated balloon:

Expand special cases:

Expand special cases under argument restrictions:

Compositions with the inverse function need PowerExpand:

Solve an equation containing EllipticF:

Numerically find a root of a transcendental equation:

Integrals:

Limits on branch cuts:

The defining integral converges only under additional conditions:

Different conventions exist for the second argument:

In traditional form the vertical separator must be used:

Nested derivatives:

Plot EllipticF at integer points: