HP HP-15C - Section 8 Program Branching and Controls; Branching

88 SectionS: Calculating in Complex Mode
Example: Approximate the integrals
f cos x C sin x
Ji = / ax and 1? = I ax.
Jl x + l/x Jl x + l/x
These integrands decay very slowly as x approaches infinity and
therefore require a long interval of integration and a long
execution time. You can expedite this calculation by deforming the ^
path of integration from the real axis into the complex plane.
According to complex variable theory, these integrals can be
combined as
+ i°° ;, <^\s complex integrand, evaluated along the line x = I and y ^ 0,
decays rapidly as y increases—like e~y.
To use the previous program to calculate both integrals at the same
time, write a subroutine to evaluate
— elZ
~ 2 + 1/2 '
Keystrokes Display
046-42,21,12 ^
047- 15
048- 43 36
049- 40 Calculates 2+ 172.
050- 43 36
051- 1
052- 42 30 Forms 0 + i.
053- 20
054- 12 Calculates e'2.
055- 34
056- 10 Calculates/(2).
057- 43 32
Approximate the complex integral by integrating the function
from 1 + Ch' to 1 + 6z using a | SCI | 2 display format to obtain three
significant digits. (The integral beyond 1 + 6z doesn't affect the
first three digits.)