DLMF:1.17.E14 (Q673): Difference between revisions

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Property / constraint
 

a > 0 𝑎 0 {\displaystyle{\displaystyle a>0}}

a>0
Property / constraint: a > 0 𝑎 0 {\displaystyle{\displaystyle a>0}} / rank
 
Normal rank

Revision as of 15:51, 30 December 2019

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DLMF:1.17.E14
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    Statements

    δ ( x - a ) = 2 x a π 0 t 2 𝗃 ( x t ) 𝗃 ( a t ) d t , Dirac-delta 𝑥 𝑎 2 𝑥 𝑎 𝜋 superscript subscript 0 superscript 𝑡 2 spherical-Bessel-J 𝑥 𝑡 spherical-Bessel-J 𝑎 𝑡 𝑡 {\displaystyle{\displaystyle\delta\left(x-a\right)=\frac{2xa}{\pi}\int_{0}^{% \infty}t^{2}\mathsf{j}_{\ell}\left(xt\right)\mathsf{j}_{\ell}\left(at\right)% \mathrm{d}t,}}
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    a > 0 𝑎 0 {\displaystyle{\displaystyle a>0}}
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