Some Sonine-Gegenbauer type integrals
The paper is devoted to series representations of Sonine-Gegenbauer type integrals of the form \[ \int_0^z \frac{C_\mu (\sqrt{\alpha^2+ at^2})} {(\alpha^2+ at^2)^{\delta/2}} \frac{D_\nu (\sqrt{\beta^2+ bt^2})} {(\beta^2+ bt^2)^{\nu/2}} t^{\lambda-1} dt, \qquad z\in \mathbb{R}\cup \{\infty\}, \] where \(C_\mu\) and \(D_\nu\) are Bessel functions. Some special cases are considered and an application of the results is given.
scientific article; zbMATH DE number 1391626
scientific article