How I can calculate this integral:
$$ \int_{-\infty}^{+\infty} \frac{\mu^x}{x!} dx$$
where $\mu$ is a constant number?
I tried to solve it using:
Gamma function of Euler
$\Gamma(x + 1) = x!$
But using this method I couldn't continue
Calculate the integral of a $x!$
0
$\begingroup$
improper-integrals
factorial
gamma-function
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0You shall check for the convergence of the integral, first of all. Most probably there are different region of convergence, or less, due to what $\mu$ can be. – 2017-01-07
1 Answers
3
It diverges. As $x\to-\infty$, the integrand grows without bound, regardless of $\mu$.