Evaluation of four irrational definite sine integrals using residue theory

摘要

This paper evaluates four irrational definite sine integrals using complex variable residue theory. A solution using this method does not require the choosing of complicated contour integration paths around the singularities and branch points of the integrand. The solutions produced are in the form of infinite series which converge rapidly. The integrals in this paper can be shown to be complete elliptic integrals of the first and second kind. In each case the Laurent series was found by re-indexing the series to find the constant co-efficient of the 1/z term.