DLMF:10.13.E11 (Q3136)

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DLMF:10.13.E11
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    Statements

    Defining formula
    ( ϑ 4 - 2 ⁢ ( ν 2 + μ 2 ) ⁢ ϑ 2 + ( ν 2 - μ 2 ) 2 ) ⁢ w + 4 ⁢ z 2 ⁢ ( ϑ + 1 ) ⁢ ( ϑ + 2 ) ⁢ w = 0 , superscript italic-ϑ 4 2 superscript 𝜈 2 superscript 𝜇 2 superscript italic-ϑ 2 superscript superscript 𝜈 2 superscript 𝜇 2 2 𝑤 4 superscript 𝑧 2 italic-ϑ 1 italic-ϑ 2 𝑤 0 {\displaystyle{\displaystyle\left(\vartheta^{4}-2(\nu^{2}+\mu^{2})\vartheta^{2% }+(\nu^{2}-\mu^{2})^{2}\right)w+4z^{2}(\vartheta+1)(\vartheta+2)w=0,}}
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    DLMF id
    DLMF:10.13.E11
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    comment
    Warning: Falling back to standard tex;
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    constraint
    w = 𝒞 ν ⁡ ( z ) ⁢ 𝒟 μ ⁢ ( z ) . 𝑤 cylinder-function 𝜈 𝑧 subscript 𝒟 𝜇 𝑧 {\displaystyle{\displaystyle w=\mathscr{C}_{\nu}\left(z\right)\mathscr{D}_{\mu% }(z).}}
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    Symbols used
    Q11430
    Defining formula
    𝒞 ν ⁡ ( z ) cylinder-function 𝜈 𝑧 {\displaystyle{\displaystyle\mathscr{C}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.Px5.p1.m3ajdec
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    Q11426
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1jdec
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    Q11427
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1hdec
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