Evaluate for complex arguments:

Evaluate to high precision:

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

Evaluate EllipticF efficiently at high precision:

Compute worst-case guaranteed intervals using Interval and CenteredInterval objects:

Or compute average case statistical intervals using Around:

Compute the elementwise values of an array:

Or compute the matrix EllipticF function using MatrixFunction:

Simple exact values are generated automatically:

Value at infinity:

Limiting values on branch cuts:

Find the root of the equation :

EllipticF is an odd function with respect to its first parameter:

Plot the elliptic integral for various values of parameter :

Plot the elliptic integral as a function of its parameter :

Plot the real part of :

Plot the imaginary part of :

is defined for all real values:

takes all real values:

EllipticF is an odd function with respect to its first parameter:

is an analytic function of :

Has no singularities or discontinuities:

is not a meromorphic function of and :

is nondecreasing on its real domain:

is injective:

is not surjective:

is neither non-negative nor non-positive:

is neither convex nor concave:

First derivative:

Higher derivatives:

Plot higher derivatives for :

Differentiate with respect to parameter :

Indefinite integral of EllipticF:

Definite integral of an odd function over an interval centered at the origin is 0:

More integrals:

Taylor expansion for EllipticF:

Plots of the first three approximations for around :

Expand in series with respect to the modulus:

Plots of the first three approximations for around :

EllipticF can be applied to power series:

The definition of the elliptic integral of the second kind:

Relation to EllipticPi:

EllipticF can be represented as a DifferentialRoot:

TraditionalForm formatting: