Evaluation of four irrational cosine definite integrals using residue theory

摘要

This paper evaluates four irrational integrals that are not part of the general category of integrals that are usually evaluated by residue theory. Each integral was solved by finding the constant contribution to the 1⧸Z term from a series expansion. This was done by reordering the infinite series so that the constant portion could be more easily observed. This approach is new and extends the domain of residue theory to new and more challenging integrals. Standard textbooks on complex variables do not attempt to solve problems of this type. It appears that this approach toward obtaining solutions is applicable to a whole class of irrational integrals that have never before been solved.