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0-a-p-1-p-2-x-2n-p-2-dx-1-lt-2n-lt-n-1-




Question Number 153893 by Tawa11 last updated on 11/Sep/21
∫_( 0) ^(  ∞) a Π_(p → 1) ^∞ (((p^2   −   x^(2n) )/p^2 ))dx,           1  <  2n  <  n  +  1
$$\int_{\:\mathrm{0}} ^{\:\:\infty} \mathrm{a}\:\underset{\mathrm{p}\:\rightarrow\:\mathrm{1}} {\overset{\infty} {\prod}}\left(\frac{\mathrm{p}^{\mathrm{2}} \:\:−\:\:\:\mathrm{x}^{\mathrm{2n}} }{\mathrm{p}^{\mathrm{2}} }\right)\mathrm{dx},\:\:\:\:\:\:\:\:\:\:\:\mathrm{1}\:\:<\:\:\mathrm{2n}\:\:<\:\:\mathrm{n}\:\:+\:\:\mathrm{1} \\ $$

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