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

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Property / Symbols used
 
Property / Symbols used: Q11428 / rank
 
Normal rank
Property / Symbols used: Q11428 / qualifier
 
test:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11428 / qualifier
 
xml-id: C10.S1.XMD3.m1kdec
Property / Symbols used
 
Property / Symbols used: Q11426 / rank
 
Normal rank
Property / Symbols used: Q11426 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11426 / qualifier
 
xml-id: C10.S1.XMD6.m1ndec
Property / Symbols used
 
Property / Symbols used: Q11427 / rank
 
Normal rank
Property / Symbols used: Q11427 / qualifier
 
test:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11427 / qualifier
 
xml-id: C10.S1.XMD7.m1mdec
Property / Symbols used
 
Property / Symbols used: expansion (locally) / rank
 
Normal rank
Property / Symbols used: expansion (locally) / qualifier
 
test:

a k ⁢ ( ν ) subscript 𝑎 𝑘 𝜈 {\displaystyle{\displaystyle a_{k}(\nu)}}

a_{k}(\nu)
Property / Symbols used: expansion (locally) / qualifier
 
xml-id: C10.S17.XMD1.m1gdec
Property / Symbols used
 
Property / Symbols used: remainder (locally) / rank
 
Normal rank
Property / Symbols used: remainder (locally) / qualifier
 
test:

R ℓ ± ⁢ ( ν , z ) superscript subscript 𝑅 ℓ plus-or-minus 𝜈 𝑧 {\displaystyle{\displaystyle R_{\ell}^{\pm}(\nu,z)}}

R_{\ell}^{\pm}(\nu,z)
Property / Symbols used: remainder (locally) / qualifier
 
xml-id: C10.S17.XMD6.m1dec

Latest revision as of 14:33, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:10.17.E17
No description defined

    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
    Q11438
    test
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C10.S1.XMD1.m1dec
    0 references
    Q11428
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C10.S1.XMD3.m1kdec
    0 references
    Q11426
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1ndec
    0 references
    Q11427
    test
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1mdec
    0 references
    expansion (locally)
    test
    a k ⁢ ( ν ) subscript 𝑎 𝑘 𝜈 {\displaystyle{\displaystyle a_{k}(\nu)}}
    xml-id
    C10.S17.XMD1.m1gdec
    0 references
    remainder (locally)
    test
    R ℓ ± ⁢ ( ν , z ) superscript subscript 𝑅 ℓ plus-or-minus 𝜈 𝑧 {\displaystyle{\displaystyle R_{\ell}^{\pm}(\nu,z)}}
    xml-id
    C10.S17.XMD6.m1dec
    0 references
     
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