Calculates the value of
$$\Gamma_1(x, \alpha) = \int_x^\infty t^{\alpha-1} e^{-it} \mathrm{d}t$$
for \(0 < \alpha < 1\) through the following relations:
$$\int_0^\infty t^{\alpha-1} e^{-it} \mathrm{d}t =
e^{-i\frac{\pi}{2}\alpha} \int_0^\infty t^{\alpha-1} e^{-t} \mathrm{d}t =
e^{-i\frac{\pi}{2}\alpha} \Gamma(\alpha).$$
obtained by contour integration, and:
$$\int_0^x t^{\alpha-1} e^{-it} \mathrm{d}t =
\int_0^x t^{\alpha-1} \mathrm{cos}(t) \mathrm{d}t -
i \int_0^x t^{\alpha-1} \mathrm{sin}(t) \mathrm{d}t =
Ci(x, \alpha) - i Si(x, \alpha)$$.
The first integral is calculated using function "tgamma" from the library
"boost::math", while the functions Ci and Si are approximated via
Taylor expansions.