DLMF:10.2.E2 (Q3006)

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DLMF:10.2.E2
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    Defining formula
    J ν ⁡ ( z ) = ( 1 2 ⁢ z ) ν ⁢ ∑ k = 0 ∞ ( - 1 ) k ⁢ ( 1 4 ⁢ z 2 ) k k ! ⁢ Γ ⁡ ( ν + k + 1 ) . Bessel-J 𝜈 𝑧 superscript 1 2 𝑧 𝜈 superscript subscript 𝑘 0 superscript 1 𝑘 superscript 1 4 superscript 𝑧 2 𝑘 𝑘 Euler-Gamma 𝜈 𝑘 1 {\displaystyle{\displaystyle J_{\nu}\left(z\right)=(\tfrac{1}{2}z)^{\nu}\sum_{% k=0}^{\infty}(-1)^{k}\frac{(\tfrac{1}{4}z^{2})^{k}}{k!\Gamma\left(\nu+k+1% \right)}.}}
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    DLMF id
    DLMF:10.2.E2
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