DLMF:13.16.E4 (Q4555): Difference between revisions

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Property / constraint
 

ℜ ⁡ ( κ - μ ) - 1 2 < 0 𝜅 𝜇 1 2 0 {\displaystyle{\displaystyle\Re(\kappa-\mu)-\tfrac{1}{2}<0}}

\realpart@@{(\kappa-\mu)-\tfrac{1}{2}}<0
Property / constraint: ℜ ⁡ ( κ - μ ) - 1 2 < 0 𝜅 𝜇 1 2 0 {\displaystyle{\displaystyle\Re(\kappa-\mu)-\tfrac{1}{2}<0}} / rank
 
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Revision as of 16:49, 30 December 2019

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DLMF:13.16.E4
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    Statements

    test
    1 Γ ⁡ ( 1 + 2 ⁢ μ ) ⁢ M κ , μ ⁡ ( z ) = z ⁢ e - 1 2 ⁢ z Γ ⁡ ( 1 2 + μ - κ ) ⁢ ∫ 0 ∞ e - t ⁢ t - κ - 1 2 ⁢ I 2 ⁢ μ ⁡ ( 2 ⁢ z ⁢ t ) ⁢ d t , 1 Euler-Gamma 1 2 𝜇 Whittaker-confluent-hypergeometric-M 𝜅 𝜇 𝑧 𝑧 superscript 𝑒 1 2 𝑧 Euler-Gamma 1 2 𝜇 𝜅 superscript subscript 0 superscript 𝑒 𝑡 superscript 𝑡 𝜅 1 2 modified-Bessel-first-kind 2 𝜇 2 𝑧 𝑡 𝑡 {\displaystyle{\displaystyle\frac{1}{\Gamma\left(1+2\mu\right)}M_{\kappa,\mu}% \left(z\right)=\frac{\sqrt{z}e^{-\frac{1}{2}z}}{\Gamma\left(\frac{1}{2}+\mu-% \kappa\right)}\*\int_{0}^{\infty}e^{-t}t^{-\kappa-\frac{1}{2}}I_{2\mu}\left(2% \sqrt{zt}\right)\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:13.16.E4
    0 references
    constraint
    ℜ ⁡ ( κ - μ ) - 1 2 < 0 𝜅 𝜇 1 2 0 {\displaystyle{\displaystyle\Re(\kappa-\mu)-\tfrac{1}{2}<0}}
    0 references
     
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