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

### 5.27.20 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.