DLMF:5.12.E12 (Q2157)

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Language	Label	Description	Also known as
English	DLMF:5.12.E12	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{P}^{(1+,0+,1-,0-)}t^{a-1}(1-t)^{b-1}\mathrm{% d}t=-4e^{\pi i(a+b)}\sin\left(\pi a\right)\sin\left(\pi b\right)\mathrm{B}% \left(a,b\right),}}

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DLMF:5.12.E12

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Defining formula

{\displaystyle{\displaystyle\mathrm{B}\left(\NVar{a},\NVar{b}\right)}}

C5.S12.E1.m2akdec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2ahdec

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Defining formula

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

C1.S4.SS4.m1akdec

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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.m2aedec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3akdec

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Defining formula

{\displaystyle{\displaystyle\sin\NVar{z}}}

C4.S14.E1.m2acdec

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Defining formula

{\displaystyle{\displaystyle a}}

C5.S1.XMD8.m1kdec

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Defining formula

{\displaystyle{\displaystyle b}}

C5.S1.XMD9.m1kdec

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Defining formula

{\displaystyle{\displaystyle P}}

C5.S12.XMD1.m1dec

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Sitelinks

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