@sym
: taylor (f) ¶@sym
: taylor (f, x) ¶@sym
: taylor (f, x, a) ¶@sym
: taylor (f, [x, y]) ¶@sym
: taylor (f, [x, y], [a, b]) ¶@sym
: taylor (…, key, value) ¶Symbolic Taylor polynomial.
If omitted, x is chosen with symvar
and a
defaults to zero.
The degree of the polynomial is controlled via the order of the remainder with a key/value pair which defaults to 6:
syms x f = exp(x); taylor(f, x, 0, 'order', 6) ⇒ (sym) 5 4 3 2 x x x x ─── + ── + ── + ── + x + 1 120 24 6 2
The degree of the returned Taylor polynomial will be (at most)
one less than ’order’. In the above example, using big O notation,
f == p + O(x^6)
.
Two-dimensional expansion:
syms x y f = exp(x*y); taylor(f, [x,y] , [0,0], 'order', 7) ⇒ (sym) 3 3 2 2 x ⋅y x ⋅y ───── + ───── + x⋅y + 1 6 2
As an alternative to passing a, you can also set the expansion point using a key/value notation:
syms x f = exp(x); taylor(f, 'expansionPoint', 1, 'order', 4) ⇒ (sym) 3 2 ℯ⋅(x - 1) ℯ⋅(x - 1) ────────── + ────────── + ℯ⋅(x - 1) + ℯ 6 2
See also: @@sym/diff.
Package: symbolic