Schlömilch's Function

$$S(\nu,z) \equiv \int_0^\infty (1+t)^{-\nu} e^{-zt}\,dt = z^{\nu-1} e^z\int_z^\infty u^{-\nu} e^{-u}\,du$$

$$= z^{\nu/2-1}e^{z/2} W_{-\nu/2,(1-\nu)/2}(z),$$

where $W_{k,m}(z)$ is the Whittaker Function.