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OrthogonalSeries

  

ApplyOperator

  

apply a differential or difference operator to a series

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

ApplyOperator(L,S)

Parameters

L

-

differential or difference operator

S

-

orthogonal series

Description

• 

The ApplyOperator function applies the operator L to the series S using the elementary operations for series: differentiation, derivative representation, and multiplication by a polynomial.

Examples

withOrthogonalSeries:

S1Create2n,LaguerreLn,1,x

S1n=02nLaguerreLn,1,x

(1)

R1ApplyOperatorx2dx27xdx+3,dx,x,S1

R1139LaguerreL0,3,x+332LaguerreL1,3,x+n=2192n+3n+32n+2n82nn+152n+1n122n+3332n+2+32n+222n+1+2n+4n242n+3n2+62n+2n2+2nn242n+1n2+92n+4n+202n+4LaguerreLn,3,x

(2)

SimplifyCoefficientsR1,simplify

139LaguerreL0,3,x+332LaguerreL1,3,x+n=2n2+26n+1392nLaguerreLn,3,x

(3)

S3Createan,m,LaguerreLn,2,x,LaguerreLm,3,y

S3m=0n=0an,mLaguerreLn,2,xLaguerreLm,3,y

(4)

RApplyOperatorxdx+ydy,dx,x,dy,y,S3

Rm=0n=0nan,m+2n4an+1,m+n+4an+2,m+man,m+2m5an,m+1+m+5an,m+2LaguerreLn,2,xLaguerreLm,3,y

(5)

SimplifyCoefficientsR,collect,a

m=0n=0n+man,m+2n4an+1,m+n+4an+2,m+2m5an,m+1+m+5an,m+2LaguerreLn,2,xLaguerreLm,3,y

(6)

S5Create1n+1,1=7,LaguerreLn,1,x

S57LaguerreL1,1,x+n=0LaguerreLn,1,xn+1

(7)

R2ApplyOperator1+xd+a,d,x,S5

R213a229LaguerreL0,2,x+7a+7LaguerreL1,2,x+n=1an+1n+21n+21n+1n+2LaguerreLn,2,x

(8)

SimplifyCoefficientsR2,simplify

13a229LaguerreL0,2,x+7a+7LaguerreL1,2,x+n=1an2LaguerreLn,2,xn+1n+2

(9)

See Also

LaguerreL

OrthogonalSeries

OrthogonalSeries[Create]

OrthogonalSeries[SimplifyCoefficients]