DLMF:10.43.E24 (Q3638)

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Language	Label	Description	Also known as
English	DLMF:10.43.E24	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{0}^{\infty}I_{\nu}\left(bt\right)\exp\left(-% p^{2}t^{2}\right)\mathrm{d}t=\frac{\sqrt{\pi}}{2p}\exp\left(\frac{b^{2}}{8p^{2% }}\right)I_{\frac{1}{2}\nu}\left(\frac{b^{2}}{8p^{2}}\right),}}

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DLMF:10.43.E24

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

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

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2afdec

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Defining formula

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

C1.S4.SS4.m1asdec

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exponential function

Defining formula

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

C4.S2.E19.m2aadec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3asdec

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modified Bessel function of the first kind

Defining formula

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

C10.S25.E2.m2aedec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1agdec

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Defining formula

{\displaystyle{\displaystyle\nu}}

C10.S1.XMD7.m1kdec

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Sitelinks

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