Integrals Related to the Error Function presents a table of integrals related to the error function, including indefinite and improper definite integrals. Most of the formulas in this book have not been presented in other tables of integrals or have been presented only for some special cases of parameters or for integration only along the real axis of the complex plane. Many of the integrals presented here cannot be obtained using a computer (except via an approximate numerical integration).
Additionally, for improper integrals, this book emphasizes the necessary and sufficient conditions for the validity of the presented formulas, including trajectory for going to infinity on the complex plane; such conditions are usually not given in computer-assisted analytical integration and often not presented in the previously published tables of integrals.
Introduction. Part 1. Indefinite integrals. Part 2. Definite integrals. Appendix: Some useful formulas for obtaining other integrals.