DLMF:13.16.E3 (Q4554)

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DLMF:13.16.E3
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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 ⁢ J 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 Bessel-J 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}}J_{2\mu}\left(2% \sqrt{zt}\right)\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:13.16.E3
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    constraint
    ℜ ⁡ ( κ + μ ) + 1 2 > 0 𝜅 𝜇 1 2 0 {\displaystyle{\displaystyle\Re(\kappa+\mu)+\tfrac{1}{2}>0}}
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