DLMF:10.13.E11 (Q3136): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11430 / rank
 
Normal rank
Property / Symbols used: Q11430 / qualifier
 
test:

𝒞 ν ⁡ ( z ) cylinder-function 𝜈 𝑧 {\displaystyle{\displaystyle\mathscr{C}_{\NVar{\nu}}\left(\NVar{z}\right)}}

\BesselC{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: Q11430 / qualifier
 
xml-id: C10.S2.Px5.p1.m3ajdec
Property / Symbols used
 
Property / Symbols used: Q11426 / rank
 
Normal rank
Property / Symbols used: Q11426 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11426 / qualifier
 
xml-id: C10.S1.XMD6.m1jdec
Property / Symbols used
 
Property / Symbols used: Q11427 / rank
 
Normal rank
Property / Symbols used: Q11427 / qualifier
 
test:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11427 / qualifier
 
xml-id: C10.S1.XMD7.m1hdec
Property / Symbols used
 
Property / Symbols used: Q11440 / rank
 
Normal rank
Property / Symbols used: Q11440 / qualifier
 
test:

ϑ = z ⁢ ( d / d z ) italic-ϑ 𝑧 derivative 𝑧 {\displaystyle{\displaystyle\vartheta=z(\ifrac{\mathrm{d}}{\mathrm{d}z})}}

\vartheta=z(\ideriv{}{z})
Property / Symbols used: Q11440 / qualifier
 
xml-id: C10.S1.XMD9.m1dec
Property / Symbols used
 
Property / Symbols used: Q11439 / rank
 
Normal rank
Property / Symbols used: Q11439 / qualifier
 
test:

𝒟 ν ⁢ ( z ) subscript 𝒟 𝜈 𝑧 {\displaystyle{\displaystyle\mathscr{D}_{\nu}(z)}}

\mathscr{D}_{\nu}(z)
Property / Symbols used: Q11439 / qualifier
 
xml-id: C10.S2.XMD1.m1bdec

Latest revision as of 14:22, 2 January 2020

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DLMF:10.13.E11
No description defined

    Statements

    test
    ( 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,}}
    0 references
    DLMF id
    DLMF:10.13.E11
    0 references
    comment
    Warning: Falling back to standard tex;
    0 references
    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).}}
    0 references
    Symbols used
    Q11430
    test
    𝒞 ν ⁡ ( z ) cylinder-function 𝜈 𝑧 {\displaystyle{\displaystyle\mathscr{C}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.Px5.p1.m3ajdec
    0 references
    Q11426
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1jdec
    0 references
    Q11427
    test
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1hdec
    0 references
    Q11440
    test
    ϑ = z ⁢ ( d / d z ) italic-ϑ 𝑧 derivative 𝑧 {\displaystyle{\displaystyle\vartheta=z(\ifrac{\mathrm{d}}{\mathrm{d}z})}}
    xml-id
    C10.S1.XMD9.m1dec
    0 references
    Q11439
    test
    𝒟 ν ⁢ ( z ) subscript 𝒟 𝜈 𝑧 {\displaystyle{\displaystyle\mathscr{D}_{\nu}(z)}}
    xml-id
    C10.S2.XMD1.m1bdec
    0 references
     
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