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OrthogonalSeries

  

Multiply

  

multiply two series

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

Multiply(S1, S2)

Parameters

S1

-

finite orthogonal series

S2

-

orthogonal series

Description

• 

The Multiply(S1, S2) function multiplies the series S2 by the finite series S1. The routine uses an adaptation of the Horner scheme.

• 

The result is expanded in terms of the polynomials of S2.

• 

This command is part of the OrthogonalSeries package, so it can be used in the form Multiply(..) only after executing the command with(OrthogonalSeries). However, it can always be accessed through the long form of the command by using OrthogonalSeries[Multiply](..).

Examples

withOrthogonalSeries:

S1ChangeBasis1+x2,LaguerreLn,13,x

S1:=379LaguerreL0,13,x143LaguerreL1,13,x+2LaguerreL2,13,x

(1)

S2Createum,Charlierm,17,x

S2:=m=0∞umCharlierm,17,x

(2)

MultiplyS1,S1

422581LaguerreL0,13,x389227LaguerreL1,13,x+5323LaguerreL2,13,x104LaguerreL3,13,x+24LaguerreL4,13,x

(3)

SimplifyCoefficientsMultiplyS1,S2,collect,u

5749u097u1+2u2Charlier0,17,x+13449u1949u0467u2+6u3Charlier1,17,x+m=2∞5749+47m+m2um+m2+3m+2u2+m+149um2+54927mum1+237m972m2um+1Charlierm,17,x

(4)

MultiplyS2,S2

Error, (in OrthogonalSeries:-Multiply) The first series  must be finite

See Also

LaguerreL

OrthogonalSeries

OrthogonalSeries[ChangeBasis]

OrthogonalSeries[Create]

OrthogonalSeries[SimplifyCoefficients]

 


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