DLMF:11.5.E6 (Q3973): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: gamma function / rank
 
Normal rank
Property / Symbols used: gamma function / qualifier
 
Defining formula:

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 14:44, 2 January 2020

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DLMF:11.5.E6
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    Statements

    Defining formula
    𝐋 ν ⁡ ( z ) = 2 ⁢ ( 1 2 ⁢ z ) ν π ⁢ Γ ⁡ ( ν + 1 2 ) ⁢ ∫ 0 π / 2 sinh ⁡ ( z ⁢ cos ⁡ θ ) ⁢ ( sin ⁡ θ ) 2 ⁢ ν ⁢ d θ , modified-Struve-L 𝜈 𝑧 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{L}_{\nu}\left(z\right)=\frac{2(\tfrac{1}{2% }z)^{\nu}}{\sqrt{\pi}\Gamma\left(\nu+\tfrac{1}{2}\right)}\int_{0}^{\pi/2}\sinh% \left(z\cos\theta\right)(\sin\theta)^{2\nu}\mathrm{d}\theta,}}
    0 references
    DLMF id
    DLMF:11.5.E6
    0 references
    constraint
    ℜ ⁡ ν > - 1 2 𝜈 1 2 {\displaystyle{\displaystyle\Re\nu>-\tfrac{1}{2}}}
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2acdec
    0 references
     
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