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

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Property / Symbols used
 
Property / Symbols used: Q12702 / rank
Normal rank
 
Property / Symbols used: Q12702 / qualifier
test:

𝖧 k ⁢ ( ℓ ; r ) subscript 𝖧 𝑘 ℓ 𝑟 {\displaystyle{\displaystyle\mathsf{H}_{k}(\ell;r)}}

\mathsf{H}_{k}(\ell;r)
 
Property / Symbols used: Q12702 / qualifier
xml-id: C33.S20.XMD3.m1bdec
 

Latest revision as of 14:39, 2 January 2020

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DLMF:33.20.E9
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    Statements

    test
    𝖧 k ⁢ ( ℓ ; r ) = ( - 1 ) ℓ + 1 ⁢ 2 π ⁢ ∑ p = 2 ⁢ k 3 ⁢ k ( 2 ⁢ | r | ) ( p + 1 ) / 2 ⁢ C k , p ⁢ K 2 ⁢ ℓ + 1 + p ⁡ ( 8 ⁢ | r | ) , subscript 𝖧 𝑘 ℓ 𝑟 superscript 1 ℓ 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 ℓ 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),}}
    0 references
    DLMF id
    DLMF:33.20.E9
    0 references
    constraint
    r < 0 𝑟 0 {\displaystyle{\displaystyle r<0}}
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    modified Bessel function of the second kind
    test
    K ν ⁡ ( z ) modified-Bessel-second-kind 𝜈 𝑧 {\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S25.E3.m2aadec
    0 references
    Q12669
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C33.S1.XMD1.m1fdec
    0 references
    Q12666
    test
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C33.S1.XMD2.m1hdec
    0 references
    Q12692
    test
    r 𝑟 {\displaystyle{\displaystyle r}}
    xml-id
    C33.S1.XMD3.m1gdec
    0 references
    Q12701
    test
    C k , p subscript 𝐶 𝑘 𝑝 {\displaystyle{\displaystyle C_{k,p}}}
    xml-id
    C33.S20.XMD2.m1ddec
    0 references
     
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