CylinderU, CylinderV - Maple Help

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CylinderU, CylinderV

Parabolic Cylinder Functions

CylinderD

Whittaker's Parabolic Function

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

CylinderU(a, x)

CylinderV(a, x)

CylinderD(a, x)

Parameters

a

-

algebraic expression (the degree)

x

-

algebraic expression (the argument)

Description

• 

CylinderU and CylinderV are the parabolic cylinder functions. They satisfy the first real standard distinct form of the Parabolic Cylinder equation:

y''14x2+ay=0

• 

CylinderD and CylinderU are related in the following way:

CylinderDa12,x=CylinderUa,x.

Examples

aaCylinderU3,0

aa:=2523/4Γ34π

(1)

evalfaa

0.4650946536

(2)

CylinderU52,x

12ⅇ14x2HermiteH2,12x2

(3)

CylinderD3.2,1

1.819497238

(4)

xCylinderUa,x

12xCylinderUa,xa+12CylinderUa+1,x

(5)

convertCylinderD32,x,CylinderU

CylinderU2,x

(6)

convertCylinderUa,x+CylinderDb,x,CylinderV

πCylinderVa,xsinπaCylinderVa,xcosπa2Γa+12+πCylinderVb12,xsinπb12πCylinderVb12,xcosπb12π2Γb

(7)

seriesCylinderV0,x,x

1223/4Γ34+1223/4Γ34πx+19623/4Γ34x4+116023/4Γ34πx5+Ox6

(8)

See Also

convert

diff

evalf

HermiteH

inifcns

series

 


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