DLMF:20.10.E4 (Q6840): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:20.10.E4	No description defined

Statements

Defining formula

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

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DLMF:20.10.E4

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Defining formula

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

C20.S2.SS1.m1acdec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2acdec

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Defining formula

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

C1.S4.SS4.m1acdec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2adec

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hyperbolic secant function

Defining formula

{\displaystyle{\displaystyle\operatorname{sech}\NVar{z}}}

C4.S28.E6.m2adec

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hyperbolic sine function

Defining formula

{\displaystyle{\displaystyle\sinh\NVar{z}}}

C4.S28.E1.m2adec

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Defining formula

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

C1.S9.E1.m2acdec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3acdec

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Defining formula

{\displaystyle{\displaystyle s}}

C20.S10.XMD1.m1dec

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Defining formula

{\displaystyle{\displaystyle\beta}}

C20.S10.XMD2.m1dec

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Defining formula

{\displaystyle{\displaystyle\ell}}

C20.S10.XMD3.m1dec

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Sitelinks

Wikipedia(0 entries)

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