DLMF:8.21.E3 (Q2724)

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Language	Label	Description	Also known as
English	DLMF:8.21.E3	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{0}^{\infty}t^{a-1}e^{\pm\mathrm{i}t}\mathrm{% d}t=e^{\pm\frac{1}{2}\pi\mathrm{i}a}\Gamma\left(a\right),}}

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DLMF:8.21.E3

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{\displaystyle{\displaystyle 0<\Re a<1}}

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Defining formula

{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

C5.S2.E1.m2adec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2abdec

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Defining formula

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

C1.S4.SS4.m1adec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2abdec

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Defining formula

{\displaystyle{\displaystyle\mathrm{i}}}

C1.S9.E1.m2abdec

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Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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