DLMF:11.5.E8 (Q3975): Difference between revisions

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Property / constraint
 

ν > - 1 𝜈 1 {\displaystyle{\displaystyle\Re\nu>-1}}

\realpart@@{\nu}>-1
Property / constraint: ν > - 1 𝜈 1 {\displaystyle{\displaystyle\Re\nu>-1}} / rank
 
Normal rank

Revision as of 16:42, 30 December 2019

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DLMF:11.5.E8
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    Statements

    ( 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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    ν > - 1 𝜈 1 {\displaystyle{\displaystyle\Re\nu>-1}}
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