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Question Number 4312 by prakash jain last updated on 08/Jan/16
![g_1 (x)=x g_n (x)=[g_(n−1) (x)]^x f(x)=lim_(n→∞) g_n (x) Is f(x) analytical for some subset of R?](Q4312.png)
$${g}_{\mathrm{1}} \left({x}\right)={x} \\ $$$${g}_{{n}} \left({x}\right)=\left[{g}_{{n}−\mathrm{1}} \left({x}\right)\right]^{{x}} \\ $$$${f}\left({x}\right)=\underset{{n}\rightarrow\infty} {\mathrm{lim}}{g}_{{n}} \left({x}\right) \\ $$$$\mathrm{Is}\:{f}\left({x}\right)\:\mathrm{analytical}\:\mathrm{for}\:\mathrm{some}\:\mathrm{subset}\:\mathrm{of}\:\mathbb{R}? \\ $$