DLMF:13.14.E33 (Q4525)

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DLMF:13.14.E33
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    Statements

    Defining formula
    W κ , μ ⁡ ( z ) = Γ ⁡ ( - 2 ⁢ μ ) Γ ⁡ ( 1 2 - μ - κ ) ⁢ M κ , μ ⁡ ( z ) + Γ ⁡ ( 2 ⁢ μ ) Γ ⁡ ( 1 2 + μ - κ ) ⁢ M κ , - μ ⁡ ( z ) . Whittaker-confluent-hypergeometric-W 𝜅 𝜇 𝑧 Euler-Gamma 2 𝜇 Euler-Gamma 1 2 𝜇 𝜅 Whittaker-confluent-hypergeometric-M 𝜅 𝜇 𝑧 Euler-Gamma 2 𝜇 Euler-Gamma 1 2 𝜇 𝜅 Whittaker-confluent-hypergeometric-M 𝜅 𝜇 𝑧 {\displaystyle{\displaystyle W_{\kappa,\mu}\left(z\right)=\frac{\Gamma\left(-2% \mu\right)}{\Gamma\left(\frac{1}{2}-\mu-\kappa\right)}M_{\kappa,\mu}\left(z% \right)+\frac{\Gamma\left(2\mu\right)}{\Gamma\left(\frac{1}{2}+\mu-\kappa% \right)}M_{\kappa,-\mu}\left(z\right).}}
    0 references
    DLMF id
    DLMF:13.14.E33
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2andec
    0 references
    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.m2apdec
    0 references
    Whittaker confluent hypergeometric function
    Defining formula
    W κ , μ ⁡ ( z ) Whittaker-confluent-hypergeometric-W 𝜅 𝜇 𝑧 {\displaystyle{\displaystyle W_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}
    xml-id
    C13.S14.E3.m2audec
    0 references
     
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