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Question Number 137420 by mnjuly1970 last updated on 02/Apr/21

$$......mathematical.........analysis\left(II\right).....$$$$provethat::$$$$\mathrm{\Omega }={\int }_{\mathbb{R}}\left(\underset{n=0}{\sum ^{\mathrm{\infty }}}\frac{{(-x^2)}^n}{{(n!)}^2}\right)dx=1$$$$..........................$$

Commented by Dwaipayan Shikari last updated on 03/Apr/21

$${\int }_{\mathbb{R}}\underset{n⩾0}{\sum ^{\mathrm{\infty }}}\frac{{(-x^2)}^n}{{(n!)}^{2s}}dx={\pi }^{1-s}$$$${\int }_{\mathbb{R}}\underset{n⩾0}{\sum ^{\mathrm{\infty }}}\frac{{(-x^2)}^n}{{(n!)}^2}=1$$

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