ABSTRACT
This chapter discusses a few of the basic mathematical questions without any indication of the physical significance of the complex variable z or the analytic function f(z). A dispersion relation is a formula for the real part of an analytic function as an integral over its imaginary part. It is an application of Cauchy's integral formula. The name dispersion relation is due to physicists and will not be found in the mathematical literature. A dispersion relation is an identity satisfied by the real and imaginary parts of a wide class of analytic functions. If some further relation is specified between the real and imaginary parts of the analytic function, the dispersion relation can be converted into a certain type of singular integral equation. A dispersion relation is an identity satisfied by a wide class of analytic functions.
