HP 48GII

3-214 Full Command and Function Reference
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 thehp49g+/hp48gII 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
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:
Γ x 1+()e
t–
t
x
td
0
∞
∫
=
and defined for other values of x by analytic continuation: Γ(x + 1) = n Γ(x)
Access: !´
L PROBABILITY ! ( ´ is the left-shift of the Pkey).
Flags: Numerical Results (-3), Underflow Exception (-20), Overflow Exception (-21)
Input/Output:
Level 1/Argument 1 Level 1/Item 1
n
→
n!
x
→
Γ (x + 1)
'symb'
→
'(symb!)'
See also: COMB, PERM
% (Percent)
Type: Function
Description: Percent Function: Returns x percent of y.
Common usage is ambiguous about some units of temperature. When ºC or ºF represents a
thermometer reading, then the temperature is a unit with an additive constant: 0 ºC=273.15 K,