DLMF:25.5.E11 (Q7624)

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Language	Label	Description	Also known as
English	DLMF:25.5.E11	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\zeta\left(s\right)=\frac{1}{2}+\frac{1}{s-1}+2% \int_{0}^{\infty}\frac{\sin\left(s\operatorname{arctan}x\right)}{(1+x^{2})^{s/% 2}(e^{2\pi x}-1)}\mathrm{d}x.}}

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DLMF:25.5.E11

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Riemann zeta function

Defining formula

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

C25.S2.E1.m2ajdec

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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.m1ajdec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2afdec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3ajdec

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Defining formula

{\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}

C4.S23.SS2.p1.m7aadec

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Defining formula

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

C4.S14.E1.m2adec

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Defining formula

{\displaystyle{\displaystyle x}}

C25.S1.XMD5.m1jdec

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Defining formula

{\displaystyle{\displaystyle s}}

C25.S1.XMD7.m1jdec

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Sitelinks

Wikipedia(0 entries)

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