Difference between revisions of "TaylorPolynomial Command"
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| − | <noinclude>{{Manual Page|version= | + | <noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|function}} |
| − | {{command|cas=true|function}} | + | ; TaylorPolynomial( <Function>, <x-Value>, <Order Number> ) |
| − | ; TaylorPolynomial | + | :Creates the power series expansion for the given function at the point ''x-Value'' to the given order. |
| − | :Creates the power series expansion for the given function | + | :{{example| 1=<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''.}} |
| − | :{{example| 1= | ||
==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= | + | :{{example| 1=<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''.}} |
| − | ;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. |
| − | :{{ | + | :{{examples| 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 ''x<sup>3</sup> sin(3) + x<sup>3</sup> cos(3) (y - 3) - x<sup>3</sup> <math>\frac{sin(3) }{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.}} | ||
Latest revision as of 09:55, 9 October 2017
- 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.
- Examples:
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 x3 sin(3) + x3 cos(3) (y - 3) - x3 \frac{sin(3) }{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.
