DLMF:10.22.E53 (Q3427)

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Language	Label	Description	Also known as
English	DLMF:10.22.E53	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{0}^{\infty}Y_{2\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)\left(I_{\nu}\left(\frac{b^{2}}{8p^{2}}\right)\tan\left(\nu\pi% \right)+\frac{1}{\pi}K_{\nu}\left(\frac{b^{2}}{8p^{2}}\right)\sec\left(\nu\pi% \right)\right),}}

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DLMF:10.22.E53

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{\displaystyle{\displaystyle|\Re\nu|<\tfrac{1}{2}}}

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

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Bessel function of the second kind

Defining formula

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

C10.S2.E3.m2ahdec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2audec

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Defining formula

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

C1.S4.SS4.m1aazdec

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exponential function

Defining formula

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

C4.S2.E19.m2abdec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3aazdec

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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.m2abdec

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modified Bessel function of the second kind

Defining formula

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

C10.S25.E3.m2abdec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1aahdec

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secant function

Defining formula

{\displaystyle{\displaystyle\sec\NVar{z}}}

C4.S14.E6.m2abdec

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tangent function

Defining formula

{\displaystyle{\displaystyle\tan\NVar{z}}}

C4.S14.E4.m2abdec

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Defining formula

{\displaystyle{\displaystyle\nu}}

C10.S1.XMD7.m1aldec

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