Reference Guide

3-250 Full Command and Function Reference
TAYLOR0
Type: Function
Description: Performs a fourth-order Taylor expansion of an expression at x = 0.
Access: Calculus, !Ö LIMITS & SERIES , P CALC 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
Type: Command
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: !Ö LIMITS & 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' n
order
→
'symb
Taylor
'
Example: The command 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