- #1
bigplanet401
- 104
- 0
Evaluate:
[tex]
\frac{1}{\sqrt{2\pi} \sigma} \int_{-\infty}^{\infty} \, dx \, exp\left[-\frac{(x - \mu)^2}{2\sigma^2}\right] \, ,
[/tex]
where [tex]$\mu$[/tex] and [tex]$\sigma$[/tex] are complex numbers.
I tried writing
[tex]
\begin{align}
\sigma &= s_1 + is_2 \,\\
\mu &= m_1 + i m_2 \, .
\end{align}
[/tex]
The integral turned into
[tex]
\int_{-\infty}^{\infty} \, dx \, e^{x(A + iB)} e^C \, ,
[/tex]
where A, B and C are constants. But then things got dark.
[tex]
\frac{1}{\sqrt{2\pi} \sigma} \int_{-\infty}^{\infty} \, dx \, exp\left[-\frac{(x - \mu)^2}{2\sigma^2}\right] \, ,
[/tex]
where [tex]$\mu$[/tex] and [tex]$\sigma$[/tex] are complex numbers.
I tried writing
[tex]
\begin{align}
\sigma &= s_1 + is_2 \,\\
\mu &= m_1 + i m_2 \, .
\end{align}
[/tex]
The integral turned into
[tex]
\int_{-\infty}^{\infty} \, dx \, e^{x(A + iB)} e^C \, ,
[/tex]
where A, B and C are constants. But then things got dark.