DLMF:10.22.E2 (Q3374): Difference between revisions

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Property / constraint
 

ν ≠ - 1 2 𝜈 1 2 {\displaystyle{\displaystyle\nu\neq-\tfrac{1}{2}}}

\nu\neq-\tfrac{1}{2}
Property / constraint: ν ≠ - 1 2 𝜈 1 2 {\displaystyle{\displaystyle\nu\neq-\tfrac{1}{2}}} / rank
 
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Revision as of 16:18, 30 December 2019

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DLMF:10.22.E2
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    Statements

    test
    ∫ z ν ⁢ 𝒞 ν ⁡ ( z ) ⁢ d z = π 1 2 ⁢ 2 ν - 1 ⁢ Γ ⁡ ( ν + 1 2 ) ⁢ z ⁢ ( 𝒞 ν ⁡ ( z ) ⁢ 𝐇 ν - 1 ⁡ ( z ) - 𝒞 ν - 1 ⁡ ( z ) ⁢ 𝐇 ν ⁡ ( z ) ) , superscript 𝑧 𝜈 cylinder-function 𝜈 𝑧 𝑧 superscript 𝜋 1 2 superscript 2 𝜈 1 Euler-Gamma 𝜈 1 2 𝑧 cylinder-function 𝜈 𝑧 Struve-H 𝜈 1 𝑧 cylinder-function 𝜈 1 𝑧 Struve-H 𝜈 𝑧 {\displaystyle{\displaystyle\int z^{\nu}\mathscr{C}_{\nu}\left(z\right)\mathrm% {d}z=\pi^{\frac{1}{2}}2^{\nu-1}\Gamma\left(\nu+\tfrac{1}{2}\right)\*z\left(% \mathscr{C}_{\nu}\left(z\right)\mathbf{H}_{\nu-1}\left(z\right)-\mathscr{C}_{% \nu-1}\left(z\right)\mathbf{H}_{\nu}\left(z\right)\right),}}
    0 references
    DLMF id
    DLMF:10.22.E2
    0 references
    constraint
    ν ≠ - 1 2 𝜈 1 2 {\displaystyle{\displaystyle\nu\neq-\tfrac{1}{2}}}
    0 references
     
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