PochhammerBasis

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PochhammerBasis - Pochhammer polynomials based at a point

	Calling Sequence
	PochhammerBasis(k, a, x)

Parameters

k	-	algebraic expression; the index
a	-	algebraic expression; the starting point
x	-	algebraic expression; the argument

Description

•	PochhammerBasis(k,a,x) = prod(x-a+j, j=0..k-1) 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 and subsequent call to , which uses Horner's method to evaluate the polynomial .

Examples

(1)

(2)

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

P := Record(Value = Default[value], Variable = x, Degree = 3, Coefficient = coe, Dimension = [1, 1], Basis = PochhammerBasis, BasisParameters = [a], IsMonic = mon, OutputOptions = [shape = [], storage = rectangular, order = Fortran_order, fill = 0, attributes = []])

(3)

(4)

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

(5)

(6)

p := b[0]*PochhammerBasis(0, a, x)+b[1]*PochhammerBasis(1, a, x)+b[2]*PochhammerBasis(2, a, x)+b[3]*PochhammerBasis(3, a, x)

(7)

(8)

(9)

	See Also
	BernsteinBasis, convert,MatrixPolynomialObject, LagrangeBasis, LinearAlgebra[CompanionMatrix], NewtonBasis, OrthogonalSeries, type,MatrixPolynomialObject