TaylorPolynomial Command

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.