DLMF:10.43.E28 (Q3642): Difference between revisions

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Latest revision as of 14:04, 2 January 2020

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Language	Label	Description	Also known as
English	DLMF:10.43.E28	No description defined

Statements

Defining formula

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

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DLMF:10.43.E28

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{\displaystyle{\displaystyle\Re\nu>-1,\Re\left(p^{2}\right)>0}}

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Defining formula

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

C1.S4.SS4.m1awdec

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exponential function

Defining formula

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

C4.S2.E19.m2acdec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3awdec

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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.m2afdec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1akdec

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Defining formula

{\displaystyle{\displaystyle\nu}}

C10.S1.XMD7.m1odec

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Sitelinks

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