DLMF:13.15.E5 (Q4530)

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DLMF:13.15.E5
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    2 μ ( 1 + 2 μ ) M κ , μ ( z ) - 2 μ ( 1 + 2 μ ) z M κ - 1 2 , μ - 1 2 ( z ) - ( κ - μ - 1 2 ) z M κ - 1 2 , μ + 1 2 ( z ) = 0 , 2 𝜇 1 2 𝜇 Whittaker-confluent-hypergeometric-M 𝜅 𝜇 𝑧 2 𝜇 1 2 𝜇 𝑧 Whittaker-confluent-hypergeometric-M 𝜅 1 2 𝜇 1 2 𝑧 𝜅 𝜇 1 2 𝑧 Whittaker-confluent-hypergeometric-M 𝜅 1 2 𝜇 1 2 𝑧 0 {\displaystyle{\displaystyle 2\mu(1+2\mu)M_{\kappa,\mu}\left(z\right)-2\mu(1+2% \mu)\sqrt{z}M_{\kappa-\frac{1}{2},\mu-\frac{1}{2}}\left(z\right)-(\kappa-\mu-% \tfrac{1}{2})\sqrt{z}M_{\kappa-\frac{1}{2},\mu+\frac{1}{2}}\left(z\right)=0,}}
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    DLMF:13.15.E5
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