DLMF:11.7.E7 (Q3996): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: gamma function / rank
 
Normal rank
Property / Symbols used: gamma function / qualifier
 
test:

Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

\EulerGamma@{\NVar{z}}
Property / Symbols used: gamma function / qualifier
 
xml-id: C5.S2.E1.m2acdec

Revision as of 13:49, 2 January 2020

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DLMF:11.7.E7
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    Statements

    test
    ∫ 0 π / 2 𝐇 ν ⁡ ( z ⁢ sin ⁡ θ ) ⁢ ( sin ⁡ θ ) ν + 1 ( cos ⁡ θ ) 2 ⁢ ν ⁢ d θ = 2 - ν π ⁢ Γ ⁡ ( 1 2 - ν ) ⁢ z ν - 1 ⁢ ( 1 - cos ⁡ z ) , superscript subscript 0 𝜋 2 Struve-H 𝜈 𝑧 𝜃 superscript 𝜃 𝜈 1 superscript 𝜃 2 𝜈 𝜃 superscript 2 𝜈 𝜋 Euler-Gamma 1 2 𝜈 superscript 𝑧 𝜈 1 1 𝑧 {\displaystyle{\displaystyle\int_{0}^{\pi/2}\mathbf{H}_{\nu}\left(z\sin\theta% \right)\frac{(\sin\theta)^{\nu+1}}{(\cos\theta)^{2\nu}}\mathrm{d}\theta=\frac{% 2^{-\nu}}{\sqrt{\pi}}\Gamma\left(\tfrac{1}{2}-\nu\right)z^{\nu-1}(1-\cos z),}}
    0 references
    DLMF id
    DLMF:11.7.E7
    0 references
    constraint
    - 3 2 < ℜ ⁡ ν < 1 2 3 2 𝜈 1 2 {\displaystyle{\displaystyle-\tfrac{3}{2}<\Re\nu<\tfrac{1}{2}}}
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2acdec
    0 references
     
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