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:

Values of OwenT at fixed points:

OwenT for symbolic a:

Values at zero:

Find the first positive maximum of OwenT[x,1 ]:

Compute the associated OwenT[x,1] function:

Plot the OwenT function for various parameters:

Plot the real part of :

Plot the imaginary part of :

Plot the real part of the function as two parameters vary:

OwenT is defined for all real values:

is defined for :

is even with respect to and odd with respect to :

OwenT may reduce to a simpler form:

OwenT is an analytic function in both its arguments:

It is not an analytic function over the complexes:

OwenT is neither non-decreasing nor non-increasing:

is not injective for :

is not surjective for :

is non-negative for :

OwenT has no singularities or discontinuities:

has branch cut discontinuities with respect to over the complexes:

OwenT is neither convex nor concave:

TraditionalForm formatting:

First derivative with respect to x:

Higher derivatives with respect to x:

Plot the higher derivatives with respect to x when a=1.5:

First derivative with respect to a:

Higher derivatives with respect to a:

Plot the higher derivatives with respect to a when x=0.5:

Compute the indefinite integral with respect to using Integrate:

Verify the antiderivative:

Compute the indefinite integral with respect to :

Verify the antiderivative:

Definite integral:

More integrals:

Find the Taylor expansion using Series:

Plots of the first three approximations around :

Taylor expansion at a generic point:

Ordinary differential equation with respect to satisfied by :

Ordinary differential equation with respect to satisfied by :

Partial differential equation satisfied by :