DLMF:10.36.E2 (Q3558)

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DLMF:10.36.E2
No description defined

    Statements

    Defining formula
    z 2 ⁢ w ′′ + z ⁢ ( 1 ± 2 ⁢ z ) ⁢ w ′ + ( ± z - ν 2 ) ⁢ w = 0 , superscript 𝑧 2 superscript 𝑤 ′′ 𝑧 plus-or-minus 1 2 𝑧 superscript 𝑤 ′ plus-or-minus 𝑧 superscript 𝜈 2 𝑤 0 {\displaystyle{\displaystyle{z^{2}w^{\prime\prime}+z(1\pm 2z)w^{\prime}+(\pm z% -\nu^{2})w=0},}}
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    DLMF id
    DLMF:10.36.E2
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    comment
    Warning: Falling back to standard tex;
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    constraint
    w = e ∓ z ⁢ 𝒵 ν ⁡ ( z ) 𝑤 superscript 𝑒 minus-or-plus 𝑧 modified-cylinder-function 𝜈 𝑧 {\displaystyle{\displaystyle w=e^{\mp z}\mathscr{Z}_{\nu}\left(z\right)}}
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    Symbols used
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
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    Q11413
    Defining formula
    𝒵 ν ⁡ ( z ) modified-cylinder-function 𝜈 𝑧 {\displaystyle{\displaystyle\mathscr{Z}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S25.Px2.p1.m3aadec
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    Q11426
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1adec
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    Q11427
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1adec
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