PochhammerBasis - Maple Help
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PochhammerBasis

Pochhammer polynomials based at a point

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

PochhammerBasis(k, a, x)

Parameters

k

-

algebraic expression; the index

a

-

algebraic expression; the starting point

x

-

algebraic expression; the argument

Description

• 

 defines the th Pochhammer polynomial of degree . The degree of the th Pochhammer polynomial is .

• 

At present, this can only be evaluated in Maple by prior use of the object-oriented representation obtained by P:=convert(p,MatrixPolynomialObject,x) and subsequent call to P:-Value(<x-value>) , which uses Horner's method to evaluate the polynomial p.

Examples

(1)

(2)

This is in effect a NewtonBasis polynomial expression on the nodes , , and .

(3)

(4)

Note that the result returned by  represents a matrix polynomial; hence these results are 1 by 1 matrices.

(5)

(6)

(7)

(8)

(9)

See Also

BernsteinBasis

convert/MatrixPolynomialObject

LagrangeBasis

LinearAlgebra[CompanionMatrix]

NewtonBasis

OrthogonalSeries

type/MatrixPolynomialObject

 


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