Question Number 216748 by sniper237 last updated on 17/Feb/25
$${Find}\:\:\int_{−\mathrm{1}} ^{\mathrm{1}} {ln}\mid\Gamma\left(\frac{\mathrm{1}}{\mathrm{2}}+{it}\right)\mid{dt} \\ $$
Answered by issac last updated on 18/Feb/25
$$\mathrm{can}'\mathrm{t}\:\mathrm{simplify} \\ $$$$\mathrm{function}\:\mathrm{ln}\left(\mid\Gamma\left(\boldsymbol{{i}}{t}+\frac{\mathrm{1}}{\mathrm{2}}\right)\mid\right) \\ $$$$\mathrm{but}…\mathrm{Approximatly}… \\ $$$$\int_{−\mathrm{1}} ^{\:\:\mathrm{1}} \:\mathrm{ln}\left(\mid\Gamma\left(\boldsymbol{{i}}{t}+\frac{\mathrm{1}}{\mathrm{2}}\right)\mid\right)\mathrm{d}{t}\approx\mathrm{0}.\mathrm{136478}…. \\ $$