(Factorial); (Percent) - HP 48gII Advanced User's Reference Manual

When executed in stack syntax, executes a complete differentiation: the expression ' symb
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
stepwise differentiation of symb
evaluation of the expression is the derivative of the argument expression symb
new subexpression representing the derivative of symb
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:
Flags: Numerical Results (-3)
Input/Output:
TAYLOR, ∫,
See also:
!

(Factorial)

Type: Function
Description: Factorial (Gamma) Function: Returns the factorial n! of a positive integer argument n, or the
gamma function (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! = (x + 1), defined for x > –1 as:
and defined for other values of x by analytic continuation: (x + 1) = n (x)
!´ L
Access:
Flags: Numerical Results (-3), Underflow Exception (-20), Overflow Exception (-21)
Input/Output:
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,
3-214 Full Command and Function Reference
, invoking the chain rule of differentiation— the result of one
1
Level 2/Argument 1 Level 1/Argument 2
'symb '
1
z
x_unit
!
PROBABILITY
Level 1/Argument 1
n
x
'symb'
' ). When executed in algebraic syntax, executes a
1
' s argument.
1
(¿is the right-shift of the Tkey).
'name'
'name'
'name'
t – x
∫
x + 1 = e t t d
0
( ´ is the left-shift of the Pkey).
' is
1
, multiplied by a
1
Level 1/Item 1
'symb '
2
0
0
Level 1/Item 1
n!
(x + 1)
'(symb!)'