DLMF:13.16.E1 (Q4552)

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DLMF:13.16.E1
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    test
    M κ , μ ⁡ ( z ) = Γ ⁡ ( 1 + 2 ⁢ μ ) ⁢ z μ + 1 2 ⁢ 2 - 2 ⁢ μ Γ ⁡ ( 1 2 + μ - κ ) ⁢ Γ ⁡ ( 1 2 + μ + κ ) ⁢ ∫ - 1 1 e 1 2 ⁢ z ⁢ t ⁢ ( 1 + t ) μ - 1 2 - κ ⁢ ( 1 - t ) μ - 1 2 + κ ⁢ d t , Whittaker-confluent-hypergeometric-M 𝜅 𝜇 𝑧 Euler-Gamma 1 2 𝜇 superscript 𝑧 𝜇 1 2 superscript 2 2 𝜇 Euler-Gamma 1 2 𝜇 𝜅 Euler-Gamma 1 2 𝜇 𝜅 superscript subscript 1 1 superscript 𝑒 1 2 𝑧 𝑡 superscript 1 𝑡 𝜇 1 2 𝜅 superscript 1 𝑡 𝜇 1 2 𝜅 𝑡 {\displaystyle{\displaystyle M_{\kappa,\mu}\left(z\right)=\frac{\Gamma\left(1+% 2\mu\right)z^{\mu+\frac{1}{2}}2^{-2\mu}}{\Gamma\left(\frac{1}{2}+\mu-\kappa% \right)\Gamma\left(\frac{1}{2}+\mu+\kappa\right)}\*\int_{-1}^{1}e^{\frac{1}{2}% zt}(1+t)^{\mu-\frac{1}{2}-\kappa}(1-t)^{\mu-\frac{1}{2}+\kappa}\mathrm{d}t,}}
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    DLMF id
    DLMF:13.16.E1
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