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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.
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Analyticity of a function in two complex variables
Let $f$ be a function defined on $\mathbb{C}^2$ given by
$$
f(s,t)=\int\limits_{-\infty}^{\infty}dk_1 \int\limits_{-\infty}^{\infty}dk_2 \int\limits_{-\infty}^{\infty}dk_3 \frac{1}{\left(\sqrt{s}-k_1\ …