DLMF:13.16.E5 (Q4556): Difference between revisions

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Property / constraint
 

ℜ ⁡ μ + 1 2 > ℜ ⁡ κ 𝜇 1 2 𝜅 {\displaystyle{\displaystyle\Re\mu+\tfrac{1}{2}>\Re\kappa}}

\realpart@@{\mu}+\tfrac{1}{2}>\realpart@@{\kappa}
Property / constraint: ℜ ⁡ μ + 1 2 > ℜ ⁡ κ 𝜇 1 2 𝜅 {\displaystyle{\displaystyle\Re\mu+\tfrac{1}{2}>\Re\kappa}} / rank
 
Normal rank

Revision as of 16:49, 30 December 2019

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DLMF:13.16.E5
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    Statements

    test
    W κ , μ ⁡ ( z ) = z μ + 1 2 ⁢ 2 - 2 ⁢ μ Γ ⁡ ( 1 2 + μ - κ ) ⁢ ∫ 1 ∞ e - 1 2 ⁢ z ⁢ t ⁢ ( t - 1 ) μ - 1 2 - κ ⁢ ( t + 1 ) μ - 1 2 + κ ⁢ d t , Whittaker-confluent-hypergeometric-W 𝜅 𝜇 𝑧 superscript 𝑧 𝜇 1 2 superscript 2 2 𝜇 Euler-Gamma 1 2 𝜇 𝜅 superscript subscript 1 superscript 𝑒 1 2 𝑧 𝑡 superscript 𝑡 1 𝜇 1 2 𝜅 superscript 𝑡 1 𝜇 1 2 𝜅 𝑡 {\displaystyle{\displaystyle W_{\kappa,\mu}\left(z\right)=\frac{z^{\mu+\frac{1% }{2}}2^{-2\mu}}{\Gamma\left(\frac{1}{2}+\mu-\kappa\right)}\*\int_{1}^{\infty}e% ^{-\frac{1}{2}zt}(t-1)^{\mu-\frac{1}{2}-\kappa}(t+1)^{\mu-\frac{1}{2}+\kappa}% \mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:13.16.E5
    0 references
    constraint
    ℜ ⁡ μ + 1 2 > ℜ ⁡ κ 𝜇 1 2 𝜅 {\displaystyle{\displaystyle\Re\mu+\tfrac{1}{2}>\Re\kappa}}
    0 references
     
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