Difference between revisions of "TaylorPolynomial Command"

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:{{example| 1=<div><code><nowiki>TaylorPolynomial[x^2, 3, 1]</nowiki></code> gives ''6 x - 9'', the power series expansion of ''x<sup>2</sup>'' at ''x = 3'' to order ''1''.</div>}}
 
:{{example| 1=<div><code><nowiki>TaylorPolynomial[x^2, 3, 1]</nowiki></code> gives ''6 x - 9'', the power series expansion of ''x<sup>2</sup>'' at ''x = 3'' to order ''1''.</div>}}
 
:{{example| 1=<div><code><nowiki>TaylorPolynomial[x^2, a, 1]</nowiki></code> gives ''-a<sup>2</sup> + 2 a x'', the power series expansion of ''x<sup>2</sup>'' at ''x = a'' to order ''1''.</div>}}
 
:{{example| 1=<div><code><nowiki>TaylorPolynomial[x^2, a, 1]</nowiki></code> gives ''-a<sup>2</sup> + 2 a x'', the power series expansion of ''x<sup>2</sup>'' at ''x = a'' to order ''1''.</div>}}
; TaylorPolynomial[Function, Variable, Number a, Number n]: Creates the power series expansion for the given function of the given variable about the point ''Variable = a'' to order ''n''.
+
; 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| 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 of ''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 ''(cos(3) x<sup>3</sup> (2 y - 6) + sin(3) x<sup>3</sup> (-y<sup>2</sup> + 6 y - 7)) / 2'', the power series expansion of ''y'' of  ''x<sup>3</sup> sin(y)'' at ''y = 3'' to order ''2''.</div>}}
+
:{{example| 1=<div><code><nowiki>TaylorPolynomial[x^3 sin(y), y, 3, 2]</nowiki></code> gives ''(cos(3) x<sup>3</sup> (2 y - 6) + sin(3) x<sup>3</sup> (-y<sup>2</sup> + 6 y - 7)) / 2'', the power series expansion with respect to ''y'' of  ''x<sup>3</sup> sin(y)'' at ''y = 3'' to order ''2''.</div>}}
 
{{note| The order n has got to be an integer greater or equal to zero.}}
 
{{note| The order n has got to be an integer greater or equal to zero.}}

Revision as of 11:16, 22 July 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.
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 (cos(3) x3 (2 y - 6) + sin(3) x3 (-y2 + 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.
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