mathematical-analysis-II-prove-that-R-n-0-x-2-n-n-2-dx-1-

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

\dots \dots m a t h e m a t i c a l \dots \dots \dots a n a l y s i s (I I) \dots . .

p r o v e t h a t ::

Ω = \int_{R} (\underset{n = 0}{\sum^{\infty}} \frac{{(- x^{2})}^{n}}{{(n!)}^{2}}) d x = 1

\dots \dots \dots \dots \dots \dots \dots \dots . .

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

\int_{R} \underset{n ⩾ 0}{\sum^{\infty}} \frac{{(- x^{2})}^{n}}{{(n!)}^{2 s}} d x = π^{1 - s}

\int_{R} \underset{n ⩾ 0}{\sum^{\infty}} \frac{{(- x^{2})}^{n}}{{(n!)}^{2}} = 1