DLMF:10.43.E25 (Q3639)

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Language	Label	Description	Also known as
English	DLMF:10.43.E25	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{0}^{\infty}K_{\nu}\left(bt\right)\exp\left(-% p^{2}t^{2}\right)\mathrm{d}t=\frac{\sqrt{\pi}}{4p}\sec\left(\tfrac{1}{2}\pi\nu% \right)\exp\left(\frac{b^{2}}{8p^{2}}\right)K_{\frac{1}{2}\nu}\left(\frac{b^{2% }}{8p^{2}}\right),}}

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DLMF:10.43.E25

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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.m2agdec

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Defining formula

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

C1.S4.SS4.m1atdec

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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.m3atdec

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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.m2akdec

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