ellipticNome

Elliptic nome

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Syntax

ellipticNome(m)

Description

ellipticNome(m) represents the elliptic nome q which is defined as

q(m)=eπK(m)K(m)

The elliptic nome q(m) is defined for complex arguments m.

|q(m)|1 holds for all m.

Environment Interactions

When called with floating-point arguments, these functions are sensitive to the environment variable DIGITS which determines the numerical working precision.

Examples

Example 1

For most exact arguments, ellipticNome returns unevaluated:

ellipticNome(1/3),
ellipticNome(2),
ellipticNome(I)

To approximate such values with floating-point numbers, use float:

float(ellipticNome(3/4))

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

ellipticNome(0.5)

For m = 0, m = 1/2, and m = 1, ellipticNome returns explicit results:

ellipticNome(0),
ellipticNome(1/2),
ellipticNome(1)

Parameters

m

An arithmetical expression specifying the parameter.

Return Values

Arithmetical expression.

See Also

MuPAD Functions