DLMF:20.10.E2 (Q6838): Difference between revisions

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Latest revision as of 14:42, 2 January 2020

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Language	Label	Description	Also known as
English	DLMF:20.10.E2	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{0}^{\infty}x^{s-1}(\theta_{3}\left(0\middle|% ix^{2}\right)-1)\mathrm{d}x=\pi^{-s/2}\Gamma\left(\tfrac{1}{2}s\right)\zeta% \left(s\right),}}

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DLMF:20.10.E2

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Defining formula

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

C5.S2.E1.m2aadec

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Defining formula

{\displaystyle{\displaystyle\theta_{\NVar{j}}\left(\NVar{z}\middle|\NVar{\tau}% \right)}}

C20.S2.SS1.m1aadec

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Riemann zeta function

Defining formula

{\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}

C25.S2.E1.m2aadec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2aadec

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Defining formula

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

C1.S4.SS4.m1aadec

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Defining formula

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

C1.S9.E1.m2aadec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3aadec

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