Evaluate numerically:

Evaluate to high precision:

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

Complex number input:

Evaluate efficiently at high precision:

Compute worst-case guaranteed intervals using Interval and CenteredInterval objects:

Or compute average-case statistical intervals using Around:

Compute the elementwise values of an array:

Or compute the matrix EllipticNomeQ function using MatrixFunction:

Values at fixed points:

Evaluate symbolically:

Value at zero:

Simple arguments evaluate automatically:

Find a value of x for which EllipticNomeQ[x]=0.1:

Plot the EllipticNomeQ function for various parameters:

Plot the real part of :

Plot the imaginary part of :

Real and complex domains of EllipticNomeQ:

Approximate function range of EllpiticNomeQ:

EllipticNomeQ threads element-wise over lists:

EllipticNomeQ is not an analytic function:

Has both singularities and discontinuities for x≥1:

EllipticNomeQ is nondecreasing over its real domain:

EllipticNomeQ is injective:

EllipticNomeQ is not surjective:

EllipticNomeQ is neither non-negative nor non-positive:

EllipticNomeQ is convex over its real domain:

TraditionalForm formatting:

First derivative with respect to m:

Higher derivatives with respect to m:

Plot the higher derivatives with respect to m:

Find the Taylor expansion using Series:

Plots of the first three approximations around :

Find the series expansion at Infinity:

Find series expansion for an arbitrary symbolic direction :

Taylor expansion at a generic point: