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Fungrim entry: 02e3d2

zeax+bdx=ebaza\int_{z}^{\infty} {e}^{-a x + b} \, dx = \frac{{e}^{b - a z}}{a}
Assumptions:aC  and  bC  and  zC  and  Re(a)>0a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \operatorname{Re}(a) > 0
\int_{z}^{\infty} {e}^{-a x + b} \, dx = \frac{{e}^{b - a z}}{a}

a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \operatorname{Re}(a) > 0
Fungrim symbol Notation Short description
Integralabf(x)dx\int_{a}^{b} f(x) \, dx Integral
Expez{e}^{z} Exponential function
Infinity\infty Positive infinity
CCC\mathbb{C} Complex numbers
ReRe(z)\operatorname{Re}(z) Real part
Source code for this entry:
    Formula(Equal(Integral(Exp(Add(Neg(Mul(a, x)), b)), For(x, z, Infinity)), Div(Exp(Sub(b, Mul(a, z))), a))),
    Variables(a, b, z),
    Assumptions(And(Element(a, CC), Element(b, CC), Element(z, CC), Greater(Re(a), 0))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC