DLMF:8.6.E2 (Q2516)

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DLMF:8.6.E2
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    Statements

    Defining formula
    γ ⁡ ( a , z ) = z 1 2 ⁢ a ⁢ ∫ 0 ∞ e - t ⁢ t 1 2 ⁢ a - 1 ⁢ J a ⁡ ( 2 ⁢ z ⁢ t ) ⁢ d t , incomplete-gamma 𝑎 𝑧 superscript 𝑧 1 2 𝑎 superscript subscript 0 superscript 𝑒 𝑡 superscript 𝑡 1 2 𝑎 1 Bessel-J 𝑎 2 𝑧 𝑡 𝑡 {\displaystyle{\displaystyle\gamma\left(a,z\right)=z^{\frac{1}{2}a}\int_{0}^{% \infty}e^{-t}t^{\frac{1}{2}a-1}J_{a}\left(2\sqrt{zt}\right)\mathrm{d}t,}}
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    DLMF id
    DLMF:8.6.E2
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    constraint
    ℜ ⁡ a > 0 𝑎 0 {\displaystyle{\displaystyle\Re a>0}}
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    Symbols used
    Bessel function of the first kind
    Defining formula
    J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E2.m2adec
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