TAYLOR0

Type:

Function

 

 

 

 

Description:

Performs a fourth-order Taylor expansion of an expression at x = 0.

 

 

Access:

Calculus, !ÖLIMITS & SERIES, PCALC L

 

 

 

Input:

An expression

 

 

 

 

Output:

The Taylor expansion of the expression.

 

 

 

Flags:

Exact mode must be set (flag –105 clear).

 

 

 

 

Numeric mode must not be set (flag –3 clear).

 

 

 

 

Radians mode must be set (flag –17 set).

 

 

 

Example:

Obtain the fourth-order Taylor series expansion of cos(x) at x=0.

 

 

Command:

TAYLOR0(COS(X))

 

 

 

 

Result:

1/24*X^4+-1/2*X^2+1

 

 

 

 

See also:

DIVPC, lim, TAYLR, SERIES

 

 

 

 

TAYLR

Command

 

 

 

 

Type:

 

 

 

 

Description:

Taylor Polynomial Command: Calculates the nth order Taylor polynomial of symb in the variable

 

global.

 

 

 

 

 

The polynomial is calculated at the point global = 0. The expression symb may have a removable

 

singularity at 0. The order, n, is the relative order of the Taylor polynomial — the difference in

 

order between the largest and smallest power of global in the polynomial.

 

 

 

TAYLR always returns a symbolic result, regardless of the state of the Numeric Results flag (–3).

Access:

!ÖLIMITS & SERIES TAYLR

( Öis the left-shift of the 4key).

Input/Output:

 

 

 

 

 

 

 

 

Level 3/Argument 1 Level 2/Argument 2

Level 1/Argument 3

 

Level 1/Item 1

 

 

 

 

 

 

 

 

 

'symb'

'global'

norder

→

'symbTaylor'

 

The command

 

 

 

Example:

sequence '1+SIN(X)^2' 'X' 5 TAYLR

 

 

 

returns '1+X^2-8/4!*X^4'.

 

 

 

 

See also:

∂, ∫, Σ

 

 

 

 

TCHEBYCHEFF

 

 

 

 

Type:

Function

 

 

 

 

Description:

Returns the nth Tchebycheff polynomial.

 

 

 

Access:

Catalog, …µ

 

 

 

 

Input:

A non-negative integer, n.

 

 

 

 

Output:

The nth Tchebycheff polynomial.

 

 

 

 

Flags:

Exact mode must be set (flag –105 clear).

 

 

 

 

Numeric mode must not be set (flag –3 clear).

 

 

 

Example:

Obtain the fourth Tchebycheff polynomial.

 

 

 

Command:

TCHEBYCHEFF(4)

 

 

 

 

Result:

8*X^4-8*X^2+1

 

 

 

 

See also:

HERMITE, LEGENDRE

 

 

 

 

 

 

 

 

 

 

 

3-250 Full Command and Function Reference