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DLMF:32.10.E27 - MaRDI portal

DLMF:32.10.E27 (Q10119)

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DLMF:32.10.E27
No description defined

    Statements

    DLMF defining formula
    ϕ ⁢ ( z ) = C 1 ⁢ M κ , μ ⁡ ( ζ ) + C 2 ⁢ W κ , μ ⁡ ( ζ ) ζ ( a - b + 1 ) / 2 ⁢ exp ⁡ ( 1 2 ⁢ ζ ) , italic-ϕ 𝑧 subscript 𝐶 1 Whittaker-confluent-hypergeometric-M 𝜅 𝜇 𝜁 subscript 𝐶 2 Whittaker-confluent-hypergeometric-W 𝜅 𝜇 𝜁 superscript 𝜁 𝑎 𝑏 1 2 1 2 𝜁 {\displaystyle{\displaystyle\phi(z)=\frac{C_{1}M_{\kappa,\mu}\left(\zeta\right% )+C_{2}W_{\kappa,\mu}\left(\zeta\right)}{\zeta^{(a-b+1)/2}}\exp\left(\tfrac{1}% {2}\zeta\right),}}
    0 references
    Symbols used
    Whittaker confluent hypergeometric function
    DLMF 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.m2adec
    0 references
    Whittaker confluent hypergeometric function
    DLMF 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.m2adec
    0 references
    exponential function
    DLMF defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2abdec
    0 references
    real
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C32.S1.XMD4.m1tdec
    0 references
    a
    DLMF defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C32.S10.XMD15.m1ddec
    0 references
    b
    DLMF defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C32.S10.XMD16.m1cdec
    0 references
    function
    DLMF defining formula
    ϕ ⁢ ( z ) italic-ϕ 𝑧 {\displaystyle{\displaystyle\phi(z)}}
    xml-id
    C32.S10.XMD18.m1adec
    0 references
    κ
    DLMF defining formula
    κ 𝜅 {\displaystyle{\displaystyle\kappa}}
    xml-id
    C32.S10.XMD19.m1dec
    0 references
    μ
    DLMF defining formula
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    xml-id
    C32.S10.XMD20.m1dec
    0 references
    constants
    DLMF defining formula
    C j subscript 𝐶 𝑗 {\displaystyle{\displaystyle C_{j}}}
    xml-id
    C32.S10.XMD21.m1dec
    0 references

    Identifiers

     
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