DLMF:10.44.E4 (Q3652)

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DLMF:10.44.E4
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    test
    ( 1 2 ⁢ z ) ν = ∑ k = 0 ∞ ( - 1 ) k ⁢ ( ν + 2 ⁢ k ) ⁢ Γ ⁡ ( ν + k ) k ! ⁢ I ν + 2 ⁢ k ⁡ ( z ) , superscript 1 2 𝑧 𝜈 superscript subscript 𝑘 0 superscript 1 𝑘 𝜈 2 𝑘 Euler-Gamma 𝜈 𝑘 𝑘 modified-Bessel-first-kind 𝜈 2 𝑘 𝑧 {\displaystyle{\displaystyle\left(\tfrac{1}{2}z\right)^{\nu}=\sum_{k=0}^{% \infty}(-1)^{k}\frac{(\nu+2k)\Gamma\left(\nu+k\right)}{k!}I_{\nu+2k}\left(z% \right),}}
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    DLMF id
    DLMF:10.44.E4
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