study-the-convergence-of-A-0-t-1-1-t-2-dt-and-find-its-value-

Tinku Tara June 4, 2023 Integration 0 Comments

Question Number 30566 by abdo imad last updated on 23/Feb/18

study the convergence of A(α) =∫_0 ^∞ (t^(α−1) /(1+t^2 ))dt and find its value.

$${study}\:{the}\:{convergence}\:{of}\:{A}\left(\alpha\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{t}^{\alpha−\mathrm{1}} }{\mathrm{1}+{t}^{\mathrm{2}} }{dt}\:{and} \\ $$$${find}\:{its}\:{value}. \\ $$

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study-the-convergence-of-A-0-t-1-1-t-2-dt-and-find-its-value-

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