DLMF:10.27.E5 (Q3495): Difference between revisions

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Property / constraint
 

n = 0 , ± 1 , ± 2 , 𝑛 0 plus-or-minus 1 plus-or-minus 2 {\displaystyle{\displaystyle n=0,\pm 1,\pm 2,\ldots}}

n=0,\pm 1,\pm 2,\dotsc
Property / constraint: n = 0 , ± 1 , ± 2 , 𝑛 0 plus-or-minus 1 plus-or-minus 2 {\displaystyle{\displaystyle n=0,\pm 1,\pm 2,\ldots}} / rank
 
Normal rank

Revision as of 16:38, 30 December 2019

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DLMF:10.27.E5
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    Statements

    K n ( z ) = ( - 1 ) n - 1 2 ( I ν ( z ) ν | ν = n + I ν ( z ) ν | ν = - n ) , modified-Bessel-second-kind 𝑛 𝑧 superscript 1 𝑛 1 2 evaluated-at partial-derivative modified-Bessel-first-kind 𝜈 𝑧 𝜈 𝜈 𝑛 evaluated-at partial-derivative modified-Bessel-first-kind 𝜈 𝑧 𝜈 𝜈 𝑛 {\displaystyle{\displaystyle K_{n}\left(z\right)=\frac{(-1)^{n-1}}{2}\*\left(% \left.\frac{\partial I_{\nu}\left(z\right)}{\partial\nu}\right|_{\nu=n}+\left.% \frac{\partial I_{\nu}\left(z\right)}{\partial\nu}\right|_{\nu=-n}\right),}}
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    n = 0 , ± 1 , ± 2 , 𝑛 0 plus-or-minus 1 plus-or-minus 2 {\displaystyle{\displaystyle n=0,\pm 1,\pm 2,\ldots}}
    0 references