DLMF:5.9.E18 (Q2107)

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Language	Label	Description	Also known as
English	DLMF:5.9.E18	No description defined

Statements

Defining formula

{\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.}}

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DLMF:5.9.E18

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Euler’s constant

Defining formula

{\displaystyle{\displaystyle\gamma}}

C5.S2.E3.m2acdec

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Defining formula

{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

C1.S4.SS4.m1aqdec

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base of natural logarithm

Defining formula

{\displaystyle{\displaystyle\mathrm{e}}}

C4.S2.E11.m2ajdec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3aqdec

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principal branch of logarithm function

Defining formula

{\displaystyle{\displaystyle\ln\NVar{z}}}

C4.S2.E2.m2addec

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Sitelinks

Wikipedia(0 entries)

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