Symbolic definite (and indefinite) integration: methods and open issues

摘要

The computation of definite integrals presents one with a variety of choices. There are various methods such as Newton-Leibniz or Slater’s convolution method. There are questions such as whether to split or merge sums, how to search for singularities on the path of integration, when to issue conditional results, how to assess (possibly conditional) convergence, and more. These various considerations moreover interact with one another in a multitude of ways. Herein we discuss these various issues and illustrate with examples.