# Fungrim entry: 9a06fb

$\int_{z}^{\infty} {x}^{c} {e}^{-a x + b} \, dx = \frac{{e}^{b}}{{a}^{c + 1}} \Gamma\!\left(c + 1, a z\right)$
Assumptions:$a \in \mathbb{R} \,\mathbin{\operatorname{and}}\, b \in \mathbb{R} \,\mathbin{\operatorname{and}}\, c \in \mathbb{R} \,\mathbin{\operatorname{and}}\, z \in \mathbb{R} \,\mathbin{\operatorname{and}}\, a > 0 \,\mathbin{\operatorname{and}}\, c > 0 \,\mathbin{\operatorname{and}}\, z > 0$
TeX:
\int_{z}^{\infty} {x}^{c} {e}^{-a x + b} \, dx = \frac{{e}^{b}}{{a}^{c + 1}} \Gamma\!\left(c + 1, a z\right)

a \in \mathbb{R} \,\mathbin{\operatorname{and}}\, b \in \mathbb{R} \,\mathbin{\operatorname{and}}\, c \in \mathbb{R} \,\mathbin{\operatorname{and}}\, z \in \mathbb{R} \,\mathbin{\operatorname{and}}\, a > 0 \,\mathbin{\operatorname{and}}\, c > 0 \,\mathbin{\operatorname{and}}\, z > 0
Definitions:
Fungrim symbol Notation Short description
Integral$\int_{a}^{b} f(x) \, dx$ Integral
Pow${a}^{b}$ Power
Exp${e}^{z}$ Exponential function
Infinity$\infty$ Positive infinity
RR$\mathbb{R}$ Real numbers
Source code for this entry:
Entry(ID("9a06fb"),
Assumptions(And(Element(a, RR), Element(b, RR), Element(c, RR), Element(z, RR), Greater(a, 0), Greater(c, 0), Greater(z, 0))))