DLMF:11.5.E1 (Q3968): Difference between revisions

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Property / constraint
 

ℜ ⁡ ν > - 1 2 𝜈 1 2 {\displaystyle{\displaystyle\Re\nu>-\tfrac{1}{2}}}

\realpart@@{\nu}>-\tfrac{1}{2}
Property / constraint: ℜ ⁡ ν > - 1 2 𝜈 1 2 {\displaystyle{\displaystyle\Re\nu>-\tfrac{1}{2}}} / rank
 
Normal rank

Revision as of 16:42, 30 December 2019

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DLMF:11.5.E1
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    Statements

    test
    𝐇 ν ⁡ ( z ) = 2 ⁢ ( 1 2 ⁢ z ) ν π ⁢ Γ ⁡ ( ν + 1 2 ) ⁢ ∫ 0 1 ( 1 - t 2 ) ν - 1 2 ⁢ sin ⁡ ( z ⁢ t ) ⁢ d t = 2 ⁢ ( 1 2 ⁢ z ) ν π ⁢ Γ ⁡ ( ν + 1 2 ) ⁢ ∫ 0 π / 2 sin ⁡ ( z ⁢ cos ⁡ θ ) ⁢ ( sin ⁡ θ ) 2 ⁢ ν ⁢ d θ , Struve-H 𝜈 𝑧 2 superscript 1 2 𝑧 𝜈 𝜋 Euler-Gamma 𝜈 1 2 superscript subscript 0 1 superscript 1 superscript 𝑡 2 𝜈 1 2 𝑧 𝑡 𝑡 2 superscript 1 2 𝑧 𝜈 𝜋 Euler-Gamma 𝜈 1 2 superscript subscript 0 𝜋 2 𝑧 𝜃 superscript 𝜃 2 𝜈 𝜃 {\displaystyle{\displaystyle\mathbf{H}_{\nu}\left(z\right)=\frac{2(\tfrac{1}{2% }z)^{\nu}}{\sqrt{\pi}\Gamma\left(\nu+\tfrac{1}{2}\right)}\int_{0}^{1}(1-t^{2})% ^{\nu-\frac{1}{2}}\sin\left(zt\right)\mathrm{d}t=\frac{2(\tfrac{1}{2}z)^{\nu}}% {\sqrt{\pi}\Gamma\left(\nu+\tfrac{1}{2}\right)}\int_{0}^{\pi/2}\sin\left(z\cos% \theta\right)(\sin\theta)^{2\nu}\mathrm{d}\theta,}}
    0 references
    DLMF id
    DLMF:11.5.E1
    0 references
    constraint
    ℜ ⁡ ν > - 1 2 𝜈 1 2 {\displaystyle{\displaystyle\Re\nu>-\tfrac{1}{2}}}
    0 references
     
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