DLMF:10.9.E22 (Q3092)

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DLMF:10.9.E22
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    Statements

    Defining formula
    J ν ⁡ ( x ) = 1 2 ⁢ π ⁢ i ⁢ ∫ - i ⁢ ∞ i ⁢ ∞ Γ ⁡ ( - t ) ⁢ ( 1 2 ⁢ x ) ν + 2 ⁢ t Γ ⁡ ( ν + t + 1 ) ⁢ d t , Bessel-J 𝜈 𝑥 1 2 𝜋 𝑖 superscript subscript 𝑖 𝑖 Euler-Gamma 𝑡 superscript 1 2 𝑥 𝜈 2 𝑡 Euler-Gamma 𝜈 𝑡 1 𝑡 {\displaystyle{\displaystyle J_{\nu}\left(x\right)=\frac{1}{2\pi i}\int_{-i% \infty}^{i\infty}\frac{\Gamma\left(-t\right)(\tfrac{1}{2}x)^{\nu+2t}}{\Gamma% \left(\nu+t+1\right)}\mathrm{d}t,}}
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    DLMF id
    DLMF:10.9.E22
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    constraint
    ℜ ⁡ ν > 0 𝜈 0 {\displaystyle{\displaystyle\Re\nu>0}}
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    ℜ ⁡ ν > 0 𝜈 0 {\displaystyle{\displaystyle\Re\nu>0}}
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