ABSTRACT
In this section we consider the Sonin integrals and some of their generalizations. Some very brief discussion concerning trigonometric Captain's integrals is also given here.
The role of the definite Sonin integrals in the following part of the course is essential. They are used in the theory of improper integrals (Section 21) as well as in the study of dual integral equations (Section 22). The definite Sonin integrals of the Struve and Lommel functions are also used in Section 21 in order to find improper integrals of these functions. The reader can pay attention to the relation of some computations given in this section with the contents of Section 14. This connection is explained by the fact that the Poisson integral is a special case of the first Sonin integral.
