DLMF:10.40.E10 (Q3588): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: modified Bessel function of the second kind / rank
 
Normal rank
Property / Symbols used: modified Bessel function of the second kind / qualifier
 
test:

K ν ⁡ ( z ) modified-Bessel-second-kind 𝜈 𝑧 {\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}

\modBesselK{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: modified Bessel function of the second kind / qualifier
 
xml-id: C10.S25.E3.m2aedec
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.m1gdec
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.m1hdec
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.m1idec
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.m1cdec
Property / Symbols used
 
Property / Symbols used: remainder (locally) / rank
 
Normal rank
Property / Symbols used: remainder (locally) / qualifier
 
test:

R ℓ ⁢ ( ν , z ) subscript 𝑅 ℓ 𝜈 𝑧 {\displaystyle{\displaystyle R_{\ell}(\nu,z)}}

R_{\ell}(\nu,z)
Property / Symbols used: remainder (locally) / qualifier
 
xml-id: C10.S40.XMD1.m1dec

Latest revision as of 13:54, 2 January 2020

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DLMF:10.40.E10
No description defined

    Statements

    test
    K ν ⁡ ( z ) = ( π 2 ⁢ z ) 1 2 ⁢ e - z ⁢ ( ∑ k = 0 ℓ - 1 a k ⁢ ( ν ) z k + R ℓ ⁢ ( ν , z ) ) , modified-Bessel-second-kind 𝜈 𝑧 superscript 𝜋 2 𝑧 1 2 superscript 𝑒 𝑧 superscript subscript 𝑘 0 ℓ 1 subscript 𝑎 𝑘 𝜈 superscript 𝑧 𝑘 subscript 𝑅 ℓ 𝜈 𝑧 {\displaystyle{\displaystyle K_{\nu}\left(z\right)=\left(\frac{\pi}{2z}\right)% ^{\frac{1}{2}}e^{-z}\left(\sum_{k=0}^{\ell-1}\frac{a_{k}(\nu)}{z^{k}}+R_{\ell}% (\nu,z)\right),}}
    0 references
    DLMF id
    DLMF:10.40.E10
    0 references
    constraint
    ℓ = 1 , 2 , … ℓ 1 2 … {\displaystyle{\displaystyle\ell=1,2,\ldots}}
    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.m2afdec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2afdec
    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.m2aedec
    0 references
    Q11428
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C10.S1.XMD3.m1gdec
    0 references
    Q11426
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1hdec
    0 references
    Q11427
    test
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1idec
    0 references
    expansion (locally)
    test
    a k ⁢ ( ν ) subscript 𝑎 𝑘 𝜈 {\displaystyle{\displaystyle a_{k}(\nu)}}
    xml-id
    C10.S17.XMD1.m1cdec
    0 references
    remainder (locally)
    test
    R ℓ ⁢ ( ν , z ) subscript 𝑅 ℓ 𝜈 𝑧 {\displaystyle{\displaystyle R_{\ell}(\nu,z)}}
    xml-id
    C10.S40.XMD1.m1dec
    0 references
     
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