DLMF:5.12.E6 (Q2151): Difference between revisions

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Latest revision as of 19:44, 1 January 2020

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Language	Label	Description	Also known as
English	DLMF:5.12.E6	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{0}^{\pi}(\sin t)^{a-1}e^{ibt}\mathrm{d}t=% \frac{\pi}{2^{a-1}}\frac{e^{i\pi b/2}}{a\mathrm{B}\left(\frac{1}{2}(a+b+1),% \frac{1}{2}(a-b+1)\right)},}}

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DLMF:5.12.E6

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{\displaystyle{\displaystyle\Re a>0}}

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Defining formula

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

C5.S12.E1.m2aedec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2acdec

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Defining formula

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

C1.S4.SS4.m1aedec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2adec

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Defining formula

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

C1.S9.E1.m2adec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3aedec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1aadec

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Defining formula

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

C4.S14.E1.m2aadec

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Defining formula

{\displaystyle{\displaystyle a}}

C5.S1.XMD8.m1edec

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Defining formula

{\displaystyle{\displaystyle b}}

C5.S1.XMD9.m1edec

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