Difference between revisions of "TaylorPolynomial Command"
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:Creates the power series expansion for the given function with respect to the given variable about the point ''Variable = a'' to order ''n''. | :Creates the power series expansion for the given function with respect to the given variable about the point ''Variable = a'' to order ''n''. | ||
:{{example| 1=<div><code><nowiki>TaylorPolynomial[x^3 sin(y), x, 3, 2]</nowiki></code> gives ''sin(y) (9 x<sup>2</sup> - 27 x + 27)'', the power series expansion with respect to ''x'' of ''x<sup>3</sup> sin(y)'' at ''x = 3'' to order ''2''.</div>}} | :{{example| 1=<div><code><nowiki>TaylorPolynomial[x^3 sin(y), x, 3, 2]</nowiki></code> gives ''sin(y) (9 x<sup>2</sup> - 27 x + 27)'', the power series expansion with respect to ''x'' of ''x<sup>3</sup> sin(y)'' at ''x = 3'' to order ''2''.</div>}} | ||
| − | :{{example| 1=<div><code><nowiki>TaylorPolynomial[x^3 sin(y), y, 3, 2]</nowiki></code> gives ''<math> | + | :{{example| 1=<div><code><nowiki>TaylorPolynomial[x^3 sin(y), y, 3, 2]</nowiki></code> gives ''<math>\frac{cos(3) x^{3} (2 y - 6) + sin(3) x^{3} (-y^{2} + 6 y - 7)}{2}</math>'' , the power series expansion with respect to ''y'' of ''x<sup>3</sup> sin(y)'' at ''y = 3'' to order ''2''.</div>}} |
{{note| 1=The order n has got to be an integer greater or equal to zero.}} | {{note| 1=The order n has got to be an integer greater or equal to zero.}} | ||
Revision as of 14:23, 5 September 2011
- TaylorPolynomial[ <Function>, <Number a>, <Number n>]
- Creates the power series expansion for the given function about the point x = a to order n.
- Example:
TaylorPolynomial[x^2, 3, 1]gives 6 x - 9, the power series expansion of x2 at x = 3 to order 1.
CAS Syntax
- TaylorPolynomial[ <Function>, <Number a>, <Number n>]
- Creates the power series expansion for the given function about the point x = a to order n.
- Example:
TaylorPolynomial[x^2, a, 1]gives -a2 + 2 a x, the power series expansion of x2 at x = a to order 1.
- TaylorPolynomial[ <Function>, <Variable>, <Number a>, <Number n>]
- Creates the power series expansion for the given function with respect to the given variable about the point Variable = a to order n.
- Example:
TaylorPolynomial[x^3 sin(y), x, 3, 2]gives sin(y) (9 x2 - 27 x + 27), the power series expansion with respect to x of x3 sin(y) at x = 3 to order 2.
- Example:
TaylorPolynomial[x^3 sin(y), y, 3, 2]gives \frac{cos(3) x^{3} (2 y - 6) + sin(3) x^{3} (-y^{2} + 6 y - 7)}{2} , the power series expansion with respect to y of x3 sin(y) at y = 3 to order 2.
Note: The order n has got to be an integer greater or equal to zero.
