DLMF:25.5.E10 (Q7623)

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Language	Label	Description	Also known as
English	DLMF:25.5.E10	No description defined

Statements

Defining formula

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

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DLMF:25.5.E10

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Riemann zeta function

Defining formula

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

C25.S2.E1.m2aidec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2adec

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cosine function

Defining formula

{\displaystyle{\displaystyle\cos\NVar{z}}}

C4.S14.E2.m2adec

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Defining formula

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

C1.S4.SS4.m1aidec

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hyperbolic cosine function

Defining formula

{\displaystyle{\displaystyle\cosh\NVar{z}}}

C4.S28.E2.m2adec

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Sitelinks

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