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ellipticE

Complete and incomplete elliptic integrals of the second kind

Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

Syntax

ellipticE(<ϕ>, m)

Description

ellipticE(m) represents the complete elliptic integral of the second kind E(m) which is defined as

E(m)=E(π2|m)=0π/21msin2θdθ

ellipticE(φ,m) represents the incomplete elliptic integral of the second kind E(φ|m) which is defined as

E(φ|m)=0φ1msin2θdθ

The elliptic integrals of the second kind are defined for complex arguments ϕ and m.

If all arguments are numerical and at least one is a floating-point value, ellipticE returns floating-point results. For most exact arguments, it returns unevaluated symbolic calls. You can approximate such results with floating-point numbers using the float function.

Environment Interactions

When called with floating-point arguments, this function is sensitive to the environment variable DIGITS which determines the numerical working precision.

Examples

Example 1

Most calls with exact arguments return themselves unevaluated. To approximate such values with floating-point numbers, use float:

ellipticE(-PI/4),
ellipticE(PI/4, I);

float(ellipticE(-PI/4)),
float(ellipticE(PI/4, I))

Alternatively, use floating-point values as arguments. If one argument is a floating-point value and the others can be converted to a floating-point values, then a floating-point result will be returned:

ellipticE(1/2),
ellipticE(1/4, I);

ellipticE(0.5),
ellipticE(0.25, I)

Some special arguments return explicit symbolic representations:

ellipticE(0),
ellipticE(1),
ellipticE(0, m),
ellipticE(p, 0)

Parameters

m

An arithmetical expression specifying the parameter.

φ

An arithmetical expression specifying the amplitude. The default is π2.

Return Values

Arithmetical expression.

See Also

MuPAD Functions

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