Hello, guys. I am trying to solve for characteristic function of normal distribution and I've got to the point where some manipulation has been made with the term in integrands exponent. And a new term of t(adsbygoogle = window.adsbygoogle || []).push({}); ^{2}σ^{2}/2 has appeared. Could you be so kind and explain that to me, please.

[tex]=Ae^{it\mu}\int_{-\infty}^{\infty}e^{-\frac{1}{c^2}(\alpha^{2}-i2t\sigma ^{2}\alpha)}d\alpha=Ae^{(it\mu-\frac{t^{2}\sigma^{2}}{2})}\int_{-\infty}^{\infty}e^{-\frac{(\alpha-it\sigma^{2})^{2}}{c^{2}}} d\alpha [/tex]

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# A Gaussian distribution characteristic function

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