DLMF:5.9.E18

MaRDI QIDQ2695

• Label: DLMF:5.9.E18

Digital Library of Mathematical Functions ID 5.9.E18

${\displaystyle{\displaystyle\gamma=-\int_{0}^{\infty}e^{-t}\ln t\mathrm{d}t=\int_{0}^{\infty}\left(\frac{1}{1+t}-e^{-t}\right)\frac{\mathrm{d}t}{t}=\int_{0}^{1}(1-e^{-t})\frac{\mathrm{d}t}{t}-\int_{1}^{\infty}e^{-t}\frac{\mathrm{d}t}{t}=\int_{0}^{\infty}\left(\frac{e^{-t}}{1-e^{-t}}-\frac{e^{-t}}{t}\right)\mathrm{d}t.}}$

Symbols List

• ${\displaystyle{\displaystyle\gamma}}$: Euler’s constant
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
 

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