- Mathematical function, suitable for both symbolic and numerical manipulation.
- satisfies the Weber differential equation .
- For certain special arguments, ParabolicCylinderD automatically evaluates to exact values.
- ParabolicCylinderD can be evaluated to arbitrary numerical precision.
- ParabolicCylinderD automatically threads over lists.
- ParabolicCylinderD[ν,z] is an entire function of z with no branch cut discontinuities.
Examplesopen allclose all
Basic Examples (5)
Plot over a subset of the reals:
Plot over a subset of the complexes:
Series expansion at the origin:
Series expansion at Infinity:
Numerical Evaluation (4)
Evaluate to high precision:
The precision of the output tracks the precision of the input:
Complex number input:
Evaluate efficiently at high precision:
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:
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:
Series Expansions (5)
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 Identities and Simplifications (2)
Generalizations & Extensions (2)
Series expansion for symbolic first argument:
Series expansion at infinity:
Find the solution of the Schrödinger equation for a quadratic oscillator for arbitrary energies:
Properties & Relations (5)