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DLMF:13.14.E30 - MaRDI portal

DLMF:13.14.E30 (Q5219)

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DLMF:13.14.E30
No description defined

    Statements

    DLMF defining formula
    đ’Č ⁥ { W Îș , ÎŒ ⁥ ( z ) , W - Îș , ÎŒ ⁥ ( e ± π ⁹ i ⁹ z ) } = e ∓ Îș ⁹ π ⁹ i . Wronskian Whittaker-confluent-hypergeometric-W 𝜅 𝜇 𝑧 Whittaker-confluent-hypergeometric-W 𝜅 𝜇 superscript 𝑒 plus-or-minus 𝜋 imaginary-unit 𝑧 superscript 𝑒 minus-or-plus 𝜅 𝜋 imaginary-unit {\displaystyle{\displaystyle\mathscr{W}\left\{W_{\kappa,\mu}\left(z\right),W_{% -\kappa,\mu}\left(e^{\pm\pi\mathrm{i}}z\right)\right\}=e^{\mp\kappa\pi\mathrm{% i}}.}}
    0 references
    Symbols used
    Whittaker confluent hypergeometric function
    DLMF defining formula
    W Îș , ÎŒ ⁥ ( z ) Whittaker-confluent-hypergeometric-W 𝜅 𝜇 𝑧 {\displaystyle{\displaystyle W_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}
    xml-id
    C13.S14.E3.m2ardec
    0 references
    Wronskian
    DLMF defining formula
    đ’Č Wronskian {\displaystyle{\displaystyle\mathscr{W}}}
    xml-id
    C1.S13.Px2.p1.m3aedec
    0 references
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2ajdec
    0 references
    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2ardec
    0 references
    imaginary unit
    DLMF defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2ahdec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1acdec
    0 references

    Identifiers

     
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