HP 15c - Manual (Page 247)

Appendix E: A Detailed Look at
f
247
format to i n or ^ n, where n is an integer,
*
implies that the
uncertainty in the function’s values is
) (
10 10 0.5 )
δ( x m n
x
   
) (
10 0.5
x m n
   
In this formula, n is the number of digits specified in the display format and
m(x) is the exponent of the function's value at x that would appear if the
value were displayed in i display format.
The uncertainty is proportional to the factor 10
m(x)
, which represents the
magnitude of the function's value at x. Therefore, i and ^ display
formats imply an uncertainty in the function that is relative to the function's
magnitude.
Similarly, if a function value is display in • n, the rounding of the
display implies that the uncertainty in the function's values is
. 10 0.5 )
δ( n
x

 
Since this uncertainty is independent of the function's magnitude, •
display format implies an uncertainty that is absolute.
Each time the f algorithm samples the function at a value of x, it also
derives a sample of
δ
(x), the uncertainty of the function's value at x. This is
calculated using the number of digits n currently specified in the display
format and (if the display format is set to i or ^) the magnitude
m(x) of the function's value at x. The number Δ, the uncertainty of the
approximation to the desired integral, is the integral
δ
(x):
* Although i 8 or 9 generally results in the same display as i 7, it will result in a smaller
uncertainty of a calculated integral. (The same is true for the ^ format.) A negative value for n (which
can be set by using the Index register) will also affect the uncertainty of an f calculation. The minimum
value for n that will affect uncertainty is -6. A number in R
I
less than -6 will be interpreted as -6.