DLMF:10.13.E5 (Q3130): Difference between revisions

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Property / constraint
 

w = z r 𝒞 ν ( λ z q ) 𝑤 superscript 𝑧 𝑟 cylinder-function 𝜈 𝜆 superscript 𝑧 𝑞 {\displaystyle{\displaystyle w=z^{r}\mathscr{C}_{\nu}\left(\lambda z^{q}\right% )}}

w=z^{r}\BesselC{\nu}@{\lambda z^{q}}
Property / constraint: w = z r 𝒞 ν ( λ z q ) 𝑤 superscript 𝑧 𝑟 cylinder-function 𝜈 𝜆 superscript 𝑧 𝑞 {\displaystyle{\displaystyle w=z^{r}\mathscr{C}_{\nu}\left(\lambda z^{q}\right% )}} / rank
 
Normal rank

Revision as of 16:16, 30 December 2019

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DLMF:10.13.E5
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    Statements

    z 2 w ′′ + ( 1 - 2 r ) z w + ( λ 2 q 2 z 2 q + r 2 - ν 2 q 2 ) w = 0 , superscript 𝑧 2 superscript 𝑤 ′′ 1 2 𝑟 𝑧 superscript 𝑤 superscript 𝜆 2 superscript 𝑞 2 superscript 𝑧 2 𝑞 superscript 𝑟 2 superscript 𝜈 2 superscript 𝑞 2 𝑤 0 {\displaystyle{\displaystyle z^{2}w^{\prime\prime}+(1-2r)zw^{\prime}+(\lambda^% {2}q^{2}z^{2q}+r^{2}-\nu^{2}q^{2})w=0,}}
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    Warning: Falling back to standard tex;
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    w = z r 𝒞 ν ( λ z q ) 𝑤 superscript 𝑧 𝑟 cylinder-function 𝜈 𝜆 superscript 𝑧 𝑞 {\displaystyle{\displaystyle w=z^{r}\mathscr{C}_{\nu}\left(\lambda z^{q}\right% )}}
    0 references