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ellipticCE

Complementary complete elliptic integral of the second kind

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Syntax

ellipticCE(m)

Description

ellipticCE(m) represents the complementary complete elliptic integral of the second kind E(m)=E(1m), where E(m) is the complete elliptic integral of the second kind:

E(m)=E(π2|m)=0π/21msin2θdθ

The complementary complete elliptic integral of the second kind is defined for a complex argument m.

For floating-point values m, ellipticCE(m) 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:

ellipticCE(PI/4);
float(ellipticCE(PI/4))

Alternatively, use a floating-point value as an argument:

ellipticCE(1/2);
ellipticCE(0.5)

ellipticCE(0) and ellipticCE(1) have special values:

ellipticCE(0)

ellipticCE(1)

Parameters

m

An arithmetical expression specifying the parameter.

Return Values

Arithmetical expression.

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