Difference between revisions of "TaylorPolynomial Command"
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| − | ; TaylorPolynomial[ <Function>, < | + | ; TaylorPolynomial[ <Function>, <x-Value>, <Order Number> ] |
| − | :Creates the power series expansion for the given function | + | :Creates the power series expansion for the given function at the point ''x-Value'' to the given order. |
| − | :{{example| 1=<div><code><nowiki>TaylorPolynomial[x^2, 3, 1]</nowiki></code> gives ''6 x - | + | :{{example| 1=<div><code><nowiki>TaylorPolynomial[x^2, 3, 1]</nowiki></code> gives ''9 + 6 (x - 3)'', the power series expansion of ''x<sup>2</sup>'' at ''x = 3'' to order ''1''.</div>}} |
==CAS Syntax== | ==CAS Syntax== | ||
| − | ; TaylorPolynomial[ < | + | ; TaylorPolynomial[ <Expression>, <x-Value>, <Order Number> ] |
| − | :Creates the power series expansion for the given | + | :Creates the power series expansion for the given expression at the point ''x-Value'' to the given order. |
| − | :{{example| 1=<div><code><nowiki>TaylorPolynomial[x^2, a, 1]</nowiki></code> gives '' | + | :{{example| 1=<div><code><nowiki>TaylorPolynomial[x^2, a, 1]</nowiki></code> gives ''a<sup>2</sup> + 2a (x - a)'', the power series expansion of ''x<sup>2</sup>'' at ''x = a'' to order ''1''.</div>}} |
| − | ;TaylorPolynomial[ < | + | ;TaylorPolynomial[ <Expression>, <Variable>, <Variable Value>, <Order Number> ] |
| − | :Creates the power series expansion for the given | + | :Creates the power series expansion for the given expression with respect to the given variable at the point ''Variable Value'' to the given order. |
| − | :{{example| 1=<div><code><nowiki>TaylorPolynomial[x^3 sin(y), x, 3, 2]</nowiki></code> gives ''sin(y) (9 x<sup>2</sup> | + | :{{example| 1=<div> |
| − | : | + | :*<code><nowiki>TaylorPolynomial[x^3 sin(y), x, 3, 2]</nowiki></code> gives ''27 sin(y) + 27 sin(y) (x - 3) + 9 sin(y) (x - 3)<sup>2</sup>'', the power series expansion with respect to ''x'' of ''x<sup>3</sup> sin(y)'' at ''x = 3'' to order ''2''. |
| − | {{note| 1=The order | + | :*<code><nowiki>TaylorPolynomial[x^3 sin(y), y, 3, 2]</nowiki></code> gives ''sin(3) x<sup>3</sup> + cos(3) x<sup>3</sup> (y - 3) - <math>\frac{sin(3) x³}{2}</math> (y - 3)<sup>2</sup>'', 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 has got to be an integer greater or equal to zero.}} | ||
Revision as of 12:59, 9 August 2013
- TaylorPolynomial[ <Function>, <x-Value>, <Order Number> ]
- Creates the power series expansion for the given function at the point x-Value to the given order.
- Example:
TaylorPolynomial[x^2, 3, 1]gives 9 + 6 (x - 3), the power series expansion of x2 at x = 3 to order 1.
CAS Syntax
- TaylorPolynomial[ <Expression>, <x-Value>, <Order Number> ]
- Creates the power series expansion for the given expression at the point x-Value to the given order.
- Example:
TaylorPolynomial[x^2, a, 1]gives a2 + 2a (x - a), the power series expansion of x2 at x = a to order 1.
- TaylorPolynomial[ <Expression>, <Variable>, <Variable Value>, <Order Number> ]
- Creates the power series expansion for the given expression with respect to the given variable at the point Variable Value to the given order.
- Example:
TaylorPolynomial[x^3 sin(y), x, 3, 2]gives 27 sin(y) + 27 sin(y) (x - 3) + 9 sin(y) (x - 3)2, the power series expansion with respect to x of x3 sin(y) at x = 3 to order 2.TaylorPolynomial[x^3 sin(y), y, 3, 2]gives sin(3) x3 + cos(3) x3 (y - 3) - \frac{sin(3) x³}{2} (y - 3)2, the power series expansion with respect to y of x3 sin(y) at y = 3 to order 2.
Note: The order has got to be an integer greater or equal to zero.
