DLMF:10.22.E51 (Q3425): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:10.22.E51	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{0}^{\infty}J_{\nu}\left(bt\right)\exp\left(-% p^{2}t^{2}\right)t^{\nu+1}\mathrm{d}t=\frac{b^{\nu}}{(2p^{2})^{\nu+1}}\exp% \left(-\frac{b^{2}}{4p^{2}}\right),}}

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DLMF:10.22.E51

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{\displaystyle{\displaystyle\Re\nu>-1}}

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{\displaystyle{\displaystyle\Re(p^{2})>0}}

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Bessel function of the first kind

Defining formula

{\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}

C10.S2.E2.m2aaldec

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Defining formula

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

C1.S4.SS4.m1aaxdec

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exponential function

Defining formula

{\displaystyle{\displaystyle\exp\NVar{z}}}

C4.S2.E19.m2adec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3aaxdec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1aafdec

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Sitelinks

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