(15c) General complex contour integration

[Brian Zilli]

The HP 15c Advanced Functions Handbook provides a program for evaluating a contour integral along a straight line segment in the complex plane and an example of its use.

In Section 1, we discuss the complex variable theory behind the example and use it to motivate the usefulness of a program for evaluating a contour integral along a general parameterized contour. In Section 2, we present such a program, and, in Section 3, we provide an example of its use. In Section 4, we present a program for approximating the derivative of a parameterized contour. Finally, in Section 5, we present a proof of a key assumption in the handbook example discussed in Section 1.


I hope this is interesting and useful to anyone interested in HP 15c programming and functions of a complex variable. Sections 1 and 5 should be useful to anyone seeking a deeper explanation of the complex variable theory underlying the "Contour Integrals" example on pp. 88-89 of the Advanced Functions Handbook.