Reference Guide

Full Command and Function Reference 3-291
flag –2 or flag –3 is set (to return numerical results), then evaluating 'SIN( π )' returns the numerical
approximation –2.06761537357E–13.
Access: !ì ( ìis the left-shift of the #key).
Flags: Symbolic Constants (–2), Numerical Results (–3)
Input/Output:
Level 1/Argument 1 Level 1/Item 1
→
'̟'
→
3.14159265359…
See also: e, i, MAXR, MINR, →Qπ
∂ (Derivative)
Type: Function
Description: Derivative Function: Takes the derivative of an expression, number, or unit object with respect to
a specified variable of differentiation.
When executed in stack syntax, ∂ executes a complete differentiation: the expression 'symb
1
' is
evaluated repeatedly until it contains no derivatives. As part of this process, if the variable of
differentiation name has a value, the final form of the expression substitutes that value substituted
for all occurrences of the variable.
The algebraic syntax for ∂ is '∂name(symb
1
'). When executed in algebraic syntax, ∂ executes a
stepwise differentiation of symb
1
, invoking the chain rule of differentiation — the result of one
evaluation of the expression is the derivative of the argument expression symb
1
, multiplied by a
new subexpression representing the derivative of symb
1
’s argument.
If ∂ is applied to a function for which the calculator does not provide a derivative, ∂ returns a new
function whose name is der followed by the original function name.
Access: …¿ (¿is the right-shift of the Tkey).
Flags: Numerical Results (–3)
Input/Output:
Level 2/Argument 1 Level 1/Argument 2 Level 1/Item 1
'symb
1
' 'name'
→
'symb
2
'
z 'name'
→
0
x_unit 'name'
→
0
Example: In Radians mode, the command sequence 'ˆX(SIN(Y))' EVAL returns 0. When Y has
the value 'X^2' , the command sequence 'SIN(Y)' 'X' ˆ returns
'COS(X^2)*(2*X)' . The differentiation has been executed in stack syntax, so that all of
the steps of differentiation have been carried out in a single operation.
See also: TAYLOR, ∫ , Σ
! (Factorial)
Type: Function
Description: Factorial (Gamma) Function: Returns the factorial n! of a positive integer argument n, or the
gamma function Γ(x+1) of a non-integer argument x.
For x ≥ 253.1190554375 or n < 0, ! causes an overflow exception (if flag –21 is set, the exception
is treated as an error). For non-integer x ≤ –254.1082426465, ! causes an underflow exception (if
flag –20 is set, the exception is treated as an error).
In algebraic syntax, ! follows its argument. Thus the algebraic syntax for the factorial of 7 is 7!.
For non-integer arguments x, x! = Γ(x + 1), defined for x > –1 as: