DLMF:11.5.E8 (Q3975)

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DLMF:11.5.E8
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    test
    ( 1 2 ⁢ x ) - ν - 1 ⁢ 𝐇 ν ⁡ ( x ) = - 1 2 ⁢ π ⁢ i ⁢ ∫ - i ⁢ ∞ i ⁢ ∞ π ⁢ csc ⁡ ( π ⁢ s ) Γ ⁡ ( 3 2 + s ) ⁢ Γ ⁡ ( 3 2 + ν + s ) ⁢ ( 1 4 ⁢ x 2 ) s ⁢ d s , superscript 1 2 𝑥 𝜈 1 Struve-H 𝜈 𝑥 1 2 𝜋 𝑖 superscript subscript 𝑖 𝑖 𝜋 𝜋 𝑠 Euler-Gamma 3 2 𝑠 Euler-Gamma 3 2 𝜈 𝑠 superscript 1 4 superscript 𝑥 2 𝑠 𝑠 {\displaystyle{\displaystyle(\tfrac{1}{2}x)^{-\nu-1}\mathbf{H}_{\nu}\left(x% \right)=-\frac{1}{2\pi i}\int_{-i\infty}^{i\infty}\frac{\pi\csc\left(\pi s% \right)}{\Gamma\left(\tfrac{3}{2}+s\right)\Gamma\left(\tfrac{3}{2}+\nu+s\right% )}(\tfrac{1}{4}x^{2})^{s}\mathrm{d}s,}}
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    DLMF id
    DLMF:11.5.E8
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