DLMF:11.10.E10 (Q4027)

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DLMF:11.10.E10
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    test
    S 1 ⁢ ( ν , z ) = ∑ k = 0 ∞ ( - 1 ) k ⁢ ( 1 2 ⁢ z ) 2 ⁢ k Γ ⁡ ( k + 1 2 ⁢ ν + 1 ) ⁢ Γ ⁡ ( k - 1 2 ⁢ ν + 1 ) , subscript 𝑆 1 𝜈 𝑧 superscript subscript 𝑘 0 superscript 1 𝑘 superscript 1 2 𝑧 2 𝑘 Euler-Gamma 𝑘 1 2 𝜈 1 Euler-Gamma 𝑘 1 2 𝜈 1 {\displaystyle{\displaystyle S_{1}(\nu,z)=\sum_{k=0}^{\infty}\frac{(-1)^{k}(% \tfrac{1}{2}z)^{2k}}{\Gamma\left(k\!+\!\tfrac{1}{2}\nu+1\right)\Gamma\left(k\!% -\!\tfrac{1}{2}\nu\!+\!1\right)},}}
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    DLMF id
    DLMF:11.10.E10
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