DLMF:20.10.E5 (Q6841)

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Language	Label	Description	Also known as
English	DLMF:20.10.E5	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{0}^{\infty}e^{-st}\theta_{3}\left(\frac{(1+% \beta)\pi}{2\ell}\middle|\frac{i\pi t}{\ell^{2}}\right)\mathrm{d}t=\int_{0}^{% \infty}e^{-st}\theta_{4}\left(\frac{\beta\pi}{2\ell}\middle|\frac{i\pi t}{\ell% ^{2}}\right)\mathrm{d}t=\frac{\ell}{\sqrt{s}}\cosh\left(\beta\sqrt{s}\right)% \operatorname{csch}\left(\ell\sqrt{s}\right).}}

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DLMF:20.10.E5

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Defining formula

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

C20.S2.SS1.m1addec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2addec

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Defining formula

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

C1.S4.SS4.m1addec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2aadec

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hyperbolic cosecant function

Defining formula

{\displaystyle{\displaystyle\operatorname{csch}\NVar{z}}}

C4.S28.E5.m2adec

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hyperbolic cosine function

Defining formula

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

C4.S28.E2.m2adec

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Defining formula

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

C1.S9.E1.m2addec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3addec

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Defining formula

{\displaystyle{\displaystyle s}}

C20.S10.XMD1.m1adec

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Defining formula

{\displaystyle{\displaystyle\beta}}

C20.S10.XMD2.m1adec

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Defining formula

{\displaystyle{\displaystyle\ell}}

C20.S10.XMD3.m1adec

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Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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