DLMF:13.23.E3 (Q4637): Difference between revisions

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Property / constraint
 

- 1 2 - ℜ ⁡ μ < ℜ ⁡ ν < ℜ ⁡ κ 1 2 𝜇 𝜈 𝜅 {\displaystyle{\displaystyle-\tfrac{1}{2}-\Re\mu<\Re\nu<\Re\kappa}}

-\tfrac{1}{2}-\realpart@@{\mu}<\realpart@@{\nu}<\realpart@@{\kappa}
Property / constraint: - 1 2 - ℜ ⁡ μ < ℜ ⁡ ν < ℜ ⁡ κ 1 2 𝜇 𝜈 𝜅 {\displaystyle{\displaystyle-\tfrac{1}{2}-\Re\mu<\Re\nu<\Re\kappa}} / rank
 
Normal rank

Revision as of 16:50, 30 December 2019

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DLMF:13.23.E3
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    Statements

    test
    1 Γ ⁡ ( 1 + 2 ⁢ μ ) ⁢ ∫ 0 ∞ e - 1 2 ⁢ t ⁢ t ν - 1 ⁢ M κ , μ ⁡ ( t ) ⁢ d t = Γ ⁡ ( μ + ν + 1 2 ) ⁢ Γ ⁡ ( κ - ν ) Γ ⁡ ( 1 2 + μ + κ ) ⁢ Γ ⁡ ( 1 2 + μ - ν ) , 1 Euler-Gamma 1 2 𝜇 superscript subscript 0 superscript 𝑒 1 2 𝑡 superscript 𝑡 𝜈 1 Whittaker-confluent-hypergeometric-M 𝜅 𝜇 𝑡 𝑡 Euler-Gamma 𝜇 𝜈 1 2 Euler-Gamma 𝜅 𝜈 Euler-Gamma 1 2 𝜇 𝜅 Euler-Gamma 1 2 𝜇 𝜈 {\displaystyle{\displaystyle\frac{1}{\Gamma\left(1+2\mu\right)}\int_{0}^{% \infty}e^{-\frac{1}{2}t}t^{\nu-1}M_{\kappa,\mu}\left(t\right)\mathrm{d}t=\frac% {\Gamma\left(\mu+\nu+\frac{1}{2}\right)\Gamma\left(\kappa-\nu\right)}{\Gamma% \left(\frac{1}{2}+\mu+\kappa\right)\Gamma\left(\frac{1}{2}+\mu-\nu\right)},}}
    0 references
    DLMF id
    DLMF:13.23.E3
    0 references
    constraint
    - 1 2 - ℜ ⁡ μ < ℜ ⁡ ν < ℜ ⁡ κ 1 2 𝜇 𝜈 𝜅 {\displaystyle{\displaystyle-\tfrac{1}{2}-\Re\mu<\Re\nu<\Re\kappa}}
    0 references
     
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