DLMF:10.22.E68 (Q3442): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:10.22.E68	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{0}^{\infty}t\exp\left(-p^{2}t^{2}\right)J_{0% }\left(at\right)Y_{0}\left(at\right)\mathrm{d}t=-\frac{1}{2\pi p^{2}}\exp\left% (-\frac{a^{2}}{2p^{2}}\right)K_{0}\left(\frac{a^{2}}{2p^{2}}\right),}}

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DLMF:10.22.E68

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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.m2abadec

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Bessel function of the second kind

Defining formula

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

C10.S2.E3.m2ajdec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2azdec

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Defining formula

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

C1.S4.SS4.m1abodec

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exponential function

Defining formula

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

C4.S2.E19.m2agdec

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