DLMF:13.23.E2 (Q4636)

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DLMF:13.23.E2
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    ∫ 0 ∞ e - z ⁢ t ⁢ t μ - 1 2 ⁢ M κ , μ ⁡ ( t ) ⁢ d t = Γ ⁡ ( 2 ⁢ μ + 1 ) ⁢ ( z + 1 2 ) - κ - μ - 1 2 ⁢ ( z - 1 2 ) κ - μ - 1 2 , superscript subscript 0 superscript 𝑒 𝑧 𝑡 superscript 𝑡 𝜇 1 2 Whittaker-confluent-hypergeometric-M 𝜅 𝜇 𝑡 𝑡 Euler-Gamma 2 𝜇 1 superscript 𝑧 1 2 𝜅 𝜇 1 2 superscript 𝑧 1 2 𝜅 𝜇 1 2 {\displaystyle{\displaystyle\int_{0}^{\infty}e^{-zt}t^{\mu-\frac{1}{2}}M_{% \kappa,\mu}\left(t\right)\mathrm{d}t=\Gamma\left(2\mu+1\right)\left(z+\tfrac{1% }{2}\right)^{-\kappa-\mu-\frac{1}{2}}\*\left(z-\tfrac{1}{2}\right)^{\kappa-\mu% -\frac{1}{2}},}}
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    DLMF:13.23.E2
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