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BUILT-IN MATHEMATICA SYMBOL

ParabolicCylinderD

gives the parabolic cylinder function

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

ParabolicCylinderD is an entire function of z with no branch cut discontinuities.

Evaluate numerically:

Plot

Evaluate numerically:

Out[1]=

Plot

Out[1]=

Out[1]=

Evaluate for complex arguments and parameters:

Evaluate to high precision:

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

Simple exact input gives exact results:

ParabolicCylinderD threads element-wise over lists:

Series expansion for symbolic first argument:

Series expansion at infinity:

Find the solution of the Schrödinger equation for a quadratic oscillator for arbitrary energies:

Use FunctionExpand to expand ParabolicCylinderD into other functions:

Integrate expressions involving ParabolicCylinderD: