DLMF:13.14.E26 (Q4518)

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DLMF:13.14.E26
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    Statements

    test
    𝒲 ⁡ { M κ , μ ⁡ ( z ) , W κ , μ ⁡ ( z ) } = - Γ ⁡ ( 1 + 2 ⁢ μ ) Γ ⁡ ( 1 2 + μ - κ ) , Wronskian Whittaker-confluent-hypergeometric-M 𝜅 𝜇 𝑧 Whittaker-confluent-hypergeometric-W 𝜅 𝜇 𝑧 Euler-Gamma 1 2 𝜇 Euler-Gamma 1 2 𝜇 𝜅 {\displaystyle{\displaystyle\mathscr{W}\left\{M_{\kappa,\mu}\left(z\right),W_{% \kappa,\mu}\left(z\right)\right\}=-\frac{\Gamma\left(1+2\mu\right)}{\Gamma% \left(\frac{1}{2}+\mu-\kappa\right)},}}
    0 references
    DLMF id
    DLMF:13.14.E26
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    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aidec
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    Whittaker confluent hypergeometric function
    test
    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.m2akdec
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    Whittaker confluent hypergeometric function
    test
    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.m2andec
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    Q10865
    test
    𝒲 Wronskian {\displaystyle{\displaystyle\mathscr{W}}}
    xml-id
    C1.S13.Px2.p1.m3aadec
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    Q11557
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1ydec
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