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DLMF:13.14.E15 - MaRDI portal

DLMF:13.14.E15 (Q5201)

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DLMF:13.14.E15
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    Statements

    DLMF defining formula
    W 1 2 ± μ + n , μ ⁡ ( z ) = ( - 1 ) n ⁢ ( 1 ± 2 ⁢ μ ) n ⁢ z 1 2 ± μ + O ⁡ ( z 3 2 ± μ ) . Whittaker-confluent-hypergeometric-W plus-or-minus 1 2 𝜇 𝑛 𝜇 𝑧 superscript 1 𝑛 Pochhammer plus-or-minus 1 2 𝜇 𝑛 superscript 𝑧 plus-or-minus 1 2 𝜇 Big-O superscript 𝑧 plus-or-minus 3 2 𝜇 {\displaystyle{\displaystyle W_{\frac{1}{2}\pm\mu+n,\mu}\left(z\right)=(-1)^{n% }{\left(1\pm 2\mu\right)_{n}}z^{\frac{1}{2}\pm\mu}+O\left(z^{\frac{3}{2}\pm\mu% }\right).}}
    0 references
    Symbols used
    order not exceeding
    DLMF defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2aadec
    0 references
    Q10733
    DLMF defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1addec
    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.m2afdec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C13.S1.XMD2.m1ddec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1ndec
    0 references

    Identifiers

     
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