DLMF:10.30.E2 (Q3514): 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.m2adec

Revision as of 12:38, 2 January 2020

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DLMF:10.30.E2
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    Statements

    test
    K ν ⁡ ( z ) ∼ 1 2 ⁢ Γ ⁡ ( ν ) ⁢ ( 1 2 ⁢ z ) - ν , asymptotically-equals modified-Bessel-second-kind 𝜈 𝑧 1 2 Euler-Gamma 𝜈 superscript 1 2 𝑧 𝜈 {\displaystyle{\displaystyle K_{\nu}\left(z\right)\sim\tfrac{1}{2}\Gamma\left(% \nu\right)(\tfrac{1}{2}z)^{-\nu},}}
    0 references
    DLMF id
    DLMF:10.30.E2
    0 references
    constraint
    ℜ ⁡ ν > 0 𝜈 0 {\displaystyle{\displaystyle\Re\nu>0}}
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aadec
    0 references
    asymptotic equality
    test
    ∼ asymptotically-equals {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.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.m2adec
    0 references
     
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