DLMF:11.10.E11 (Q4028)

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DLMF:11.10.E11
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    S 2 ( ν , z ) = k = 0 ( - 1 ) k ( 1 2 z ) 2 k + 1 Γ ( k + 1 2 ν + 3 2 ) Γ ( k - 1 2 ν + 3 2 ) . subscript 𝑆 2 𝜈 𝑧 superscript subscript 𝑘 0 superscript 1 𝑘 superscript 1 2 𝑧 2 𝑘 1 Euler-Gamma 𝑘 1 2 𝜈 3 2 Euler-Gamma 𝑘 1 2 𝜈 3 2 {\displaystyle{\displaystyle S_{2}(\nu,z)=\sum_{k=0}^{\infty}\frac{(-1)^{k}(% \tfrac{1}{2}z)^{2k+1}}{\Gamma\left(k\!+\!\tfrac{1}{2}\nu\!+\!\tfrac{3}{2}% \right)\Gamma\left(k\!-\!\tfrac{1}{2}\nu\!+\!\tfrac{3}{2}\right)}.}}
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