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ParabolicCylinderD

ParabolicCylinderD
gives the parabolic cylinder function .
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • satisfies the Weber differential equation .
  • For certain special arguments, ParabolicCylinderD automatically evaluates to exact values.
Evaluate numerically:
Plot :
Evaluate numerically:
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Click for copyable input
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Plot :
In[1]:=
Click for copyable input
Out[1]=
 
In[1]:=
Click for copyable input
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:
TraditionalForm formatting:
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:
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