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:

ParabolicCylinderD can be used with Interval and CenteredInterval objects:

Compute average-case statistical intervals using Around:

Compute the elementwise values of an array:

Or compute the matrix ParabolicCylinderD function using MatrixFunction:

ParabolicCylinderD for symbolic parameters:

Value at zero:

Limiting value at infinity:

Find the first positive maximum of ParabolicCylinderD:

Evaluate for half-integer parameters:

Plot the ParabolicCylinderD function for integer () and half-integer () orders:

Plot the real part of :

Plot the imaginary part of :

Plot as real parts of two parameters vary:

Types 2 and 3 of ParabolicCylinderD function have different branch cut structures:

ParabolicCylinderD is defined for all real and complex values:

ParabolicCylinderD threads elementwise over lists:

is an analytic function of :

is neither non-decreasing nor non-increasing for :

is not injective for :

ParabolicCylinderD is not surjective:

is neither non-negative nor non-positive for :

ParabolicCylinderD has no singularities or discontinuities:

is neither convex nor concave for :

TraditionalForm formatting:

First derivative with respect to z:

Higher derivatives with respect to z

Plot the higher derivatives with respect to z when ν=2:

Formula for the derivative with respect to z:

Find the Taylor expansion using Series:

Plots of the first three approximations around :

General term in the series expansion using SeriesCoefficient:

Find the series expansion at Infinity:

Find series expansion for an arbitrary symbolic direction :

Taylor expansion at a generic point:

Function identity:

Recurrence identities: