Application - HP -15C Advanced Functions Handbook

60 Section 2: Working With \7j]
The HP-15C readily handles this integral. Don't worry about
\/l — u
2
as u approaches 1 because the figures lost to roundoff
aren't needed.
Application
The following program calculates the values of four special
functions for any argument x: ^
i c
x
P ( x ) = J e~*
/2
dt (normal distribution
2ir
~°° function)
Q(x) = 1 — P ( x ) = J e~
f /2
dt (complementary normal
distribution function)
2 C
x 2
erf(^) = — — I e
t
dt (errorfunction)
^^
:
*
/
o
2 r°° ,
2
erfc(x) = 1 — erf(^) = —j=J e
l
dt (corriplementary error
V
77
-
x
function)
The program calculates these functions using the transformation
u — e'
1
whenever|x\ 1.6 .
The function value is returned in the X-register, and the
uncertainty of the integral is returned in the Y-register. (The
uncertainty of the function value is approximately the same order
of magnitude as the number in the Y-register.) The original
argument is available in register R
0
.
^
The program has the following characteristics:
• The display format specifies the accuracy of the integrand in
the same way as it does for | 7 T| itself. However, if you specify
an unnecessarily large number of display digits, the
calculation will be prolonged.
• Small function values, such as Q(20), P(-20), and erfc(10), are ^
accurately computed as quickly as moderate values.
'-