# Calculate integral involving upper incomplete Gamma function

I need to calculate the following integral:

$$\int_{z/x}^{0}e^{-\frac{y}{b_n}}y^l\Gamma(c,ky)dy$$, with $$z<0,z\in R,x>0,x\in R,b_n>0,b_n \in R,l \geq0,l\in Z,k<0,k\in R,c\geq1,c\in Z$$

I searched in Books https://www.sciencedirect.com/book/9780123849335/table-of-integrals-series-and-products, http://people.math.sfu.ca/~cbm/aands/intro.htm for integrals involving the $$\Gamma()$$ function, but i can't find an expressions that solves this kind of integration

• It's highly unlikely that this integral has a closed form. However, have you tried using the integral definition for the incomplete Gamma and then changing the order of integration? – Yuriy S May 10 at 11:26