6.27.20  Rewriting in terms of the powers of (x-a): ptayl

The ptayl command finds the Taylor expansion for a polynomial (which will be finite).

• ptayl takes two arguments:
  • P, a polynomial given by a symbolic expression or by the list of its coefficients.
  • a, a number.
• ptayl(P,a) returns the polynomial T such that P(x) = T(x−a).

Examples.

• Input:
  ptayl(x^2+2*x+1,2)
  Output, the polynomial T:

  x2+6 x+9

• Input:
  ptayl([1,2,1],2)
  Output:

  ⎡ ⎣

  1,6,9

  ⎤ ⎦

  i.e.; x²+2x+1=(x−2)²+6(x−2)+9.