$\mathrm{PochhammerBasis}\left(k,a,x\right)=\prod _{j=0}^{k-1}\left(x+a+j\right)$ defines the $k$th Pochhammer polynomial of degree $n$. The degree of the $k$th Pochhammer polynomial is $k$.

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.

$a≔'a'$

$a≔a$

$p≔3\mathrm{PochhammerBasis}\left(0\&comma;a\&comma;x\right)+5\mathrm{PochhammerBasis}\left(2\&comma;a\&comma;x\right)+7\mathrm{PochhammerBasis}\left(3\&comma;a\&comma;x\right)$

$p≔3\mathrm{PochhammerBasis}\left(0\&comma;a\&comma;x\right)+5\mathrm{PochhammerBasis}\left(2\&comma;a\&comma;x\right)+7\mathrm{PochhammerBasis}\left(3\&comma;a\&comma;x\right)$

$P≔\mathrm{convert}\left(p\&comma;\mathrm{MatrixPolynomialObject}\&comma;x\right)$

$P≔\mathrm{Record}\left(\mathrm{Value}={\mathrm{Default}}_{\mathrm{value}}\&comma;\mathrm{Variable}=x\&comma;\mathrm{Degree}=3\&comma;\mathrm{Coefficient}=\mathrm{coe}\&comma;\mathrm{Dimension}=\left[1\&comma;1\right]\&comma;\mathrm{Basis}=\mathrm{PochhammerBasis}\&comma;\mathrm{BasisParameters}=\left[a\right]\&comma;\mathrm{IsMonic}=\mathrm{mon}\&comma;\mathrm{OutputOptions}=\left[\mathrm{shape}=\left[\right]\&comma;\mathrm{storage}=\mathrm{rectangular}\&comma;\mathrm{order}=\mathrm{Fortran\_order}\&comma;\mathrm{fill}=0\&comma;\mathrm{attributes}=\left[\right]\right]\right)$

$P:-\mathrm{Degree}\left(\right)$

$3$

$P:-\mathrm{Value}\left(x\right)\left[1,1\right]$

$\left(x+a\right)\left(x+a+1\right)\left(7x+7a+19\right)+3$

$a≔'a'$

$a≔a$

$p≔\mathrm{add}\left(b\left[k\right]\mathrm{PochhammerBasis}\left(k\&comma;a\&comma;x\right)\&comma;k=0..3\right)$

$p≔b_0\mathrm{PochhammerBasis}\left(0\&comma;a\&comma;x\right)+b_1\mathrm{PochhammerBasis}\left(1\&comma;a\&comma;x\right)+b_2\mathrm{PochhammerBasis}\left(2\&comma;a\&comma;x\right)+b_3\mathrm{PochhammerBasis}\left(3\&comma;a\&comma;x\right)$

$P≔\mathrm{convert}\left(p\&comma;\mathrm{MatrixPolynomialObject}\&comma;x\right)$

$P≔\mathrm{Record}\left(\mathrm{Value}={\mathrm{Default}}_{\mathrm{value}}\&comma;\mathrm{Variable}=x\&comma;\mathrm{Degree}=3\&comma;\mathrm{Coefficient}=\mathrm{coe}\&comma;\mathrm{Dimension}=\left[1\&comma;1\right]\&comma;\mathrm{Basis}=\mathrm{PochhammerBasis}\&comma;\mathrm{BasisParameters}=\left[a\right]\&comma;\mathrm{IsMonic}=\mathrm{mon}\&comma;\mathrm{OutputOptions}=\left[\mathrm{shape}=\left[\right]\&comma;\mathrm{storage}=\mathrm{rectangular}\&comma;\mathrm{order}=\mathrm{Fortran\_order}\&comma;\mathrm{fill}=0\&comma;\mathrm{attributes}=\left[\right]\right]\right)$

$\mathrm{collect}\left(P:-\mathrm{Value}\left(t\right)\left[1,1\right]\&comma;\left[\mathrm{seq}\left(b\left[k\right]\&comma;k=0..3\right)\right]\&comma;\mathrm{factor}\right)$

$b_0+\left(t+a\right)b_1+\left(t+a\right)\left(t+a+1\right)b_2+\left(t+a\right)\left(t+a+1\right)\left(t+a+2\right)b_3$