DLMF:10.13.E10 (Q3135): Difference between revisions

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Property / constraint
 

w = z 𝒞 ν ( z ) 𝒟 ν ( z ) 𝑤 𝑧 cylinder-function 𝜈 𝑧 subscript 𝒟 𝜈 𝑧 {\displaystyle{\displaystyle w=z\mathscr{C}_{\nu}\left(z\right)\mathscr{D}_{% \nu}(z)}}

w=z\BesselC{\nu}@{z}\mathscr{D}_{\nu}(z)
Property / constraint: w = z 𝒞 ν ( z ) 𝒟 ν ( z ) 𝑤 𝑧 cylinder-function 𝜈 𝑧 subscript 𝒟 𝜈 𝑧 {\displaystyle{\displaystyle w=z\mathscr{C}_{\nu}\left(z\right)\mathscr{D}_{% \nu}(z)}} / rank
 
Normal rank

Revision as of 16:17, 30 December 2019

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DLMF:10.13.E10
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    Statements

    z 3 w ′′′ + z ( 4 z 2 + 1 - 4 ν 2 ) w + ( 4 ν 2 - 1 ) w = 0 , superscript 𝑧 3 superscript 𝑤 ′′′ 𝑧 4 superscript 𝑧 2 1 4 superscript 𝜈 2 superscript 𝑤 4 superscript 𝜈 2 1 𝑤 0 {\displaystyle{\displaystyle{z^{3}w^{\prime\prime\prime}+z(4z^{2}+1-4\nu^{2})w% ^{\prime}+(4\nu^{2}-1)w=0},}}
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    Warning: Falling back to standard tex;
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    w = z 𝒞 ν ( z ) 𝒟 ν ( z ) 𝑤 𝑧 cylinder-function 𝜈 𝑧 subscript 𝒟 𝜈 𝑧 {\displaystyle{\displaystyle w=z\mathscr{C}_{\nu}\left(z\right)\mathscr{D}_{% \nu}(z)}}
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