DLMF:10.43.E19 (Q3633): Difference between revisions

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Property / constraint
 

| ℜ ⁡ ν | < ℜ ⁡ μ 𝜈 𝜇 {\displaystyle{\displaystyle|\Re\nu|<\Re\mu}}

|\realpart@@{\nu}|<\realpart@@{\mu}
Property / constraint: | ℜ ⁡ ν | < ℜ ⁡ μ 𝜈 𝜇 {\displaystyle{\displaystyle|\Re\nu|<\Re\mu}} / rank
 
Normal rank

Revision as of 17:40, 30 December 2019

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DLMF:10.43.E19
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    Statements

    test
    ∫ 0 ∞ t μ - 1 ⁢ K ν ⁡ ( t ) ⁢ d t = 2 μ - 2 ⁢ Γ ⁡ ( 1 2 ⁢ μ - 1 2 ⁢ ν ) ⁢ Γ ⁡ ( 1 2 ⁢ μ + 1 2 ⁢ ν ) , superscript subscript 0 superscript 𝑡 𝜇 1 modified-Bessel-second-kind 𝜈 𝑡 𝑡 superscript 2 𝜇 2 Euler-Gamma 1 2 𝜇 1 2 𝜈 Euler-Gamma 1 2 𝜇 1 2 𝜈 {\displaystyle{\displaystyle\int_{0}^{\infty}t^{\mu-1}K_{\nu}\left(t\right)% \mathrm{d}t=2^{\mu-2}\Gamma\left(\tfrac{1}{2}\mu-\tfrac{1}{2}\nu\right)\Gamma% \left(\tfrac{1}{2}\mu+\tfrac{1}{2}\nu\right),}}
    0 references
    DLMF id
    DLMF:10.43.E19
    0 references
    constraint
    | ℜ ⁡ ν | < ℜ ⁡ μ 𝜈 𝜇 {\displaystyle{\displaystyle|\Re\nu|<\Re\mu}}
    0 references
     
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