DLMF:10.17.E17 (Q3186): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: rescaled terminant function / rank
 
Normal rank
Property / Symbols used: rescaled terminant function / qualifier
 
test:

G p ⁡ ( z ) rescaled-terminant-function 𝑝 𝑧 {\displaystyle{\displaystyle G_{\NVar{p}}\left(\NVar{z}\right)}}

\scterminant{\NVar{p}}@{\NVar{z}}
Property / Symbols used: rescaled terminant function / qualifier
 
xml-id: C9.S7.E22.m2aadec

Revision as of 14:32, 2 January 2020

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DLMF:10.17.E17
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    Statements

    test
    R ℓ ± ⁢ ( ν , z ) = ( - 1 ) ℓ ⁢ 2 ⁢ cos ⁡ ( ν ⁢ π ) ⁢ ( ∑ k = 0 m - 1 ( ± i ) k ⁢ a k ⁢ ( ν ) z k ⁢ G ℓ - k ⁡ ( ∓ 2 ⁢ i ⁢ z ) + R m , ℓ ± ⁢ ( ν , z ) ) , superscript subscript 𝑅 ℓ plus-or-minus 𝜈 𝑧 superscript 1 ℓ 2 𝜈 𝜋 superscript subscript 𝑘 0 𝑚 1 superscript plus-or-minus 𝑖 𝑘 subscript 𝑎 𝑘 𝜈 superscript 𝑧 𝑘 rescaled-terminant-function ℓ 𝑘 minus-or-plus 2 𝑖 𝑧 superscript subscript 𝑅 𝑚 ℓ plus-or-minus 𝜈 𝑧 {\displaystyle{\displaystyle R_{\ell}^{\pm}(\nu,z)=(-1)^{\ell}2\cos\left(\nu% \pi\right)\*\left(\sum_{k=0}^{m-1}(\pm i)^{k}\frac{a_{k}(\nu)}{z^{k}}G_{\ell-k% }\left(\mp 2iz\right)+R_{m,\ell}^{\pm}(\nu,z)\right),}}
    0 references
    DLMF id
    DLMF:10.17.E17
    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.m2aldec
    0 references
    cosine function
    test
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2addec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2ahdec
    0 references
    rescaled terminant function
    test
    G p ⁡ ( z ) rescaled-terminant-function 𝑝 𝑧 {\displaystyle{\displaystyle G_{\NVar{p}}\left(\NVar{z}\right)}}
    xml-id
    C9.S7.E22.m2aadec
    0 references
     
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