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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