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OrthogonalSeries

  

SimplifyCoefficients

  

simplify the coefficients of an orthogonal series

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

SimplifyCoefficients(S, funct, collect_expr, other_args)

Parameters

S

-

orthogonal series

funct

-

name chosen from: collect, expand, factor, normal, and simplify

collect_expr

-

(optional) expression(s) to be collected

other_args

-

(optional) complementary arguments if funct is collect

Description

• 

The SimplifyCoefficients(S, funct) calling sequence applies the funct function, where funct is not collect, to the coefficients of the series S (both particular and general coefficients).

• 

The SimplifyCoefficients(S, collect, collect_expr, other_args) function applies the collect function to the coefficients of the series S (both particular and general coefficients). The user must specify the expression(s) to be collected by collect_expr. The user can specify a function to be applied to the collected expressions by other_args.

Examples

withOrthogonalSeries:

RCreate1a,a2,1a+1,GegenbauerCn,23,x

R:=GegenbauerC0,23,xa+a2GegenbauerC1,23,x+GegenbauerC2,23,xa+1

(1)

resDerivateR,x,operator=struct,root=1

res:=144541/3π3a2Γ56JacobiP0,16,76,xΓ232+41541/3π3a2Γ56Γ2325941/3π3Γ56Γ232a+1JacobiP1,16,76,x+203941/3π3Γ56JacobiP2,16,76,xΓ232a+1

(2)

SimplifyCoefficientsres,normal

144541/3π3a2Γ56JacobiP0,16,76,xΓ232+14541/3π3Γ5612a3+12a225JacobiP1,16,76,xΓ232a+1+203941/3π3Γ56JacobiP2,16,76,xΓ232a+1

(3)

SimplifyCoefficientsres,simplify

1415a2JacobiP0,16,76,x+11512a3+12a225JacobiP1,16,76,xa+1+2013JacobiP2,16,76,xa+1

(4)

coefunun+1n2+un+2unnn+1

coef:=unun+1n2+un+2unnn+1

(5)

R1Createcoef,n=1..∞,GegenbauerCn,a,x

R1:=n=1∞unun+1n2+un+2unnn+1GegenbauerCn,a,x

(6)

SimplifyCoefficientsR1,collect,u

n=1∞1n21nn+1unun+1n2+un+2nn+1GegenbauerCn,a,x

(7)

SimplifyCoefficientsR1,collect,u,normal

n=1∞unn2n+1un+1n2+un+2nn+1GegenbauerCn,a,x

(8)

See Also

GegenbauerC

JacobiP

OrthogonalSeries

OrthogonalSeries[Create]

OrthogonalSeries[Derivate]

 


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