DLMF:10.14.E2 (Q3139): Difference between revisions

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‎Changed an Item: Add constraint
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Property / Symbols used
 
Property / Symbols used: Q11427 / rank
 
Normal rank
Property / Symbols used: Q11427 / qualifier
 
Defining formula:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11427 / qualifier
 
xml-id: C10.S1.XMD7.m1adec

Latest revision as of 15:22, 2 January 2020

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DLMF:10.14.E2
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    Statements

    Defining formula
    0 < J ν ⁡ ( ν ) < 2 1 3 3 2 3 ⁢ Γ ⁡ ( 2 3 ) ⁢ ν 1 3 , 0 Bessel-J 𝜈 𝜈 superscript 2 1 3 superscript 3 2 3 Euler-Gamma 2 3 superscript 𝜈 1 3 {\displaystyle{\displaystyle 0<J_{\nu}\left(\nu\right)<\frac{2^{\frac{1}{3}}}{% 3^{\frac{2}{3}}\Gamma\left(\tfrac{2}{3}\right)\nu^{\frac{1}{3}}},}}
    0 references
    DLMF id
    DLMF:10.14.E2
    0 references
    constraint
    ν > 0 𝜈 0 {\displaystyle{\displaystyle\nu>0}}
    0 references
    Symbols used
    Bessel function of the first kind
    Defining formula
    J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E2.m2aadec
    0 references
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2adec
    0 references
    Q11427
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1adec
    0 references
     
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