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OrthogonalSeries

  

Degree

  

return the degree of a series with respect to one or more variables

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

Degree(S, x)

Degree(S, [x1,.., xn])

Degree(S)

Parameters

S

-

orthogonal series

x, x1, .., xn

-

names

Description

• 

If S is a finite series, then the Degree(S, x) calling sequence returns the degree of S with respect to the variable x. If S is an infinite series, then the result is infinity.

• 

The Degree(S, [x1,.., xn]) calling sequence returns [Degree(S, x1),..., Degree(S, xn)].

• 

The Degree(S) calling sequence returns the maximum degree of S with respect to its variables. This allows the user to test whether a series is finite.

Examples

withOrthogonalSeries:

SCreate0,0=3,1,2=1,3,2=α,GegenbauerCn,1,x,LaguerreLm,1,y

S:=3GegenbauerC0,1,xLaguerreL0,1,yGegenbauerC1,1,xLaguerreL2,1,y+αGegenbauerC3,1,xLaguerreL2,1,y

(1)

DegreeS,x;DegreeS,y;DegreeS,x,y

3

2

3,2

(2)

DegreeS

3

(3)

S1Create1n2,n=1..∞,ChebyshevTn,x

S1:=n=1∞ChebyshevTn,xn2

(4)

DegreeS1,x;DegreeS1,y;DegreeS1

∞

0

∞

(5)

S2Create0=1,N=2,1n2,n=3..8,ChebyshevTn,x

S2:=ChebyshevT0,x+2ChebyshevTN,x+n=38ChebyshevTn,xn2

(6)

DegreeS2

max8,N

(7)

See Also

ChebyshevT

GegenbauerC

LaguerreL

OrthogonalSeries

OrthogonalSeries[Create]

 


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