CylinderU, CylinderV
Parabolic Cylinder Functions
CylinderD
Whittaker's Parabolic Function
Calling Sequence
Parameters
Description
Examples
CylinderU(a, x)
CylinderV(a, x)
CylinderD(a, x)
a
-
algebraic expression (the degree)
x
algebraic expression (the argument)
CylinderU and CylinderV are the parabolic cylinder functions. They satisfy the first real standard distinct form of the Parabolic Cylinder equation:
y''−x24+ay=0
CylinderD and CylinderU are related in the following way:
CylinderD−a−12,x=CylinderUa,x.
aa≔CylinderU3,0
aa≔2234Γ345π
evalfaa
0.4650946536
CylinderU−52,x
ⅇ−x24HermiteH2,x222
CylinderD3.2,1
−1.819497238
diffCylinderUa,x,x
−xCylinderUa,x2−a+12CylinderUa+1,x
convertCylinderD32,x,CylinderU
CylinderU−2,x
convertCylinderUa,x+CylinderDb,x,CylinderV
πCylinderVa,−x−sinaπCylinderVa,xcosaπ2Γa+12+πCylinderV−b−12,−x−sin−b−12πCylinderV−b−12,xcos−b−12π2Γ−b
seriesCylinderV0,x,x
2342Γ34+12234Γ34πx+196234Γ34x4+1160234Γ34πx5+Ox6
See Also
convert
diff
evalf
HermiteH
inifcns
series
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