In this chapter we will present various results concerning Neumann, Kapteyn and Schlömilch series with members containing functions from the Bessel functions family (Bessel functions of the first and second kind, modified Bessel functions of the first and second kind, Struve functions, modified Struve functions etc.). In Sects. 5.7–5.9 we consider Dini series and Jacobi polynomials, respectively. Next section is devoted to summations of Schlömilch series which members contain some von Lommel functions of the first kind. Section 5.11 finishes this chapter with Neumann–Meijer G series results.