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$$ a^{x+yi} = \sum_{n=0}^\infty \frac{\left( \int_1^a \! \frac{x}{t}\,dt \, \right)^n}{n!} \left( \sum_{n=0}^\infty \frac{(-1)^n\left( \int_1^a \! \frac{y}{t}\,dt \, \right)^{2n}}{(2n)!} +i\sum_{n=0}^\infty \frac{(-1)^n\left( \int_1^a \! \frac{y}{t}\,dt \, \right)^{2n+1}}{(2n+1)!} \right)$$

$$ a^z_z$$

$$ \Gamma(z) = \int_0^\infty t^{z-1}\,e^{-t}\,dt$$