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ellipticCK

Complementary complete elliptic integral of the first kind

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Syntax

ellipticCK(m)

Description

ellipticCK(m) represents the complementary complete elliptic integral of the first kind K(m)=K(1m), where K(m) is the complete elliptic integral of the first kind:

K(m)=F(π2|m)=0π/211msin2θdθ

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

For floating-point values m, ellipticCK(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:

ellipticCK(PI/4);
float(ellipticCK(PI/4))

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

ellipticCK(1/2);
ellipticCK(0.5)

ellipticCK(1) has a special value:

ellipticCK(1)

Parameters

m

An arithmetical expression specifying the parameter.

Return Values

Arithmetical expression.

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