DLMF:1.17.E14 (Q673)

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DLMF:1.17.E14
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    Statements

    test
    δ ⁡ ( x - a ) = 2 ⁢ x ⁢ a π ⁢ ∫ 0 ∞ t 2 ⁢ 𝗃 ℓ ⁡ ( x ⁢ t ) ⁢ 𝗃 ℓ ⁡ ( a ⁢ t ) ⁢ d t , Dirac-delta 𝑥 𝑎 2 𝑥 𝑎 𝜋 superscript subscript 0 superscript 𝑡 2 spherical-Bessel-J ℓ 𝑥 𝑡 spherical-Bessel-J ℓ 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,}}
    0 references
    DLMF id
    DLMF:1.17.E14
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    constraint
    a > 0 𝑎 0 {\displaystyle{\displaystyle a>0}}
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