Built-in Mathematica Symbol

EllipticNomeQ

EllipticNomeQ[m]
gives the nome q corresponding to the parameter m in an elliptic function.

MORE INFORMATION

Mathematical function, suitable for both symbolic and numerical manipulation.

EllipticNomeQ is related to EllipticK by .

EllipticNomeQ[m] has a branch cut discontinuity in the complex m plane running from to .

For certain special arguments, EllipticNomeQ automatically evaluates to exact values.

EllipticNomeQ can be evaluated to arbitrary numerical precision.

EllipticNomeQ automatically threads over lists.

EXAMPLES

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Basic Examples (3)

Series expansion:

Scope (4)

Simple arguments evaluate automatically:

Evaluate to high precision:

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

EllipticNomeQ threads element-wise over lists:

TraditionalForm formatting:

Generalizations & Extensions (1)

EllipticNomeQ can be applied to power series:

Applications (1)

Plot EllipticNomeQ over the complex plane:

Properties & Relations (5)

Use FullSimplify to simplify expressions containing EllipticNomeQ:

Compose with inverse functions:

Find the derivative:

Symbolically solve a transcendental equation:

Numerically find a root of a transcendental equation:

Possible Issues (1)

For most named special functions, the direct function is single-valued and the inverse is multi-valued. EllipticNomeQ is a multi-valued function and the inverse function, InverseEllipticNomeQ, is single-valued. As a result, the following is correct everywhere:

Neat Examples (1)

Riemann surface of EllipticNomeQ: