DLMF:33.20.E9 (Q9678): Difference between revisions

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Property / constraint
 

r < 0 𝑟 0 {\displaystyle{\displaystyle r<0}}

r<0
Property / constraint: r < 0 𝑟 0 {\displaystyle{\displaystyle r<0}} / rank
 
Normal rank

Revision as of 18:29, 30 December 2019

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DLMF:33.20.E9
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    Statements

    𝖧 k ( ; r ) = ( - 1 ) + 1 2 π p = 2 k 3 k ( 2 | r | ) ( p + 1 ) / 2 C k , p K 2 + 1 + p ( 8 | r | ) , subscript 𝖧 𝑘 𝑟 superscript 1 1 2 𝜋 superscript subscript 𝑝 2 𝑘 3 𝑘 superscript 2 𝑟 𝑝 1 2 subscript 𝐶 𝑘 𝑝 modified-Bessel-second-kind 2 1 𝑝 8 𝑟 {\displaystyle{\displaystyle{\sf H}_{k}(\ell;r)=(-1)^{\ell+1}\frac{2}{\pi}\sum% _{p=2k}^{3k}(2|r|)^{(p+1)/2}C_{k,p}K_{2\ell+1+p}\left(\sqrt{8|r|}\right),}}
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    r < 0 𝑟 0 {\displaystyle{\displaystyle r<0}}
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