The incomplete gamma function expressed as a sum of Macdonald functions (Q5937374)

The author uses the expansion of the incomplete gamma function defined by \[ \gamma(\nu,z)=\sqrt{{2\over\pi}}\int_0^z s^{\nu-1/2} K_{1/2}(s) ds,\quad \Re \nu>0, \] in terms of the modified Bessel functions of the second kind \(K_{n+1/2}(z)\). This expansion allows to evaluate different types of integrals of interest in atomic physics.