DLMF:13.15.E6 (Q4531)

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DLMF:13.15.E6
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    Statements

    Defining formula
    2 ⁢ μ ⁢ ( 1 + 2 ⁢ μ ) ⁢ z ⁢ M κ + 1 2 , μ - 1 2 ⁡ ( z ) + ( z - 2 ⁢ μ ) ⁢ ( 1 + 2 ⁢ μ ) ⁢ M κ , μ ⁡ ( z ) + ( κ - μ - 1 2 ) ⁢ z ⁢ M κ - 1 2 , μ + 1 2 ⁡ ( z ) = 0 , 2 𝜇 1 2 𝜇 𝑧 Whittaker-confluent-hypergeometric-M 𝜅 1 2 𝜇 1 2 𝑧 𝑧 2 𝜇 1 2 𝜇 Whittaker-confluent-hypergeometric-M 𝜅 𝜇 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)\sqrt{z}M_{\kappa+\frac{1}{2},\mu-% \frac{1}{2}}\left(z\right)+(z-2\mu)(1+2\mu)M_{\kappa,\mu}\left(z\right)+(% \kappa-\mu-\tfrac{1}{2})\sqrt{z}M_{\kappa-\frac{1}{2},\mu+\frac{1}{2}}\left(z% \right)=0,}}
    0 references
    DLMF id
    DLMF:13.15.E6
    0 references
    Symbols used
    Whittaker confluent hypergeometric function
    Defining formula
    M κ , μ ⁡ ( z ) Whittaker-confluent-hypergeometric-M 𝜅 𝜇 𝑧 {\displaystyle{\displaystyle M_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}
    xml-id
    C13.S14.E2.m2aedec
    0 references
    Q11557
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1edec
    0 references
     
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