DLMF:11.11.E19 (Q4085): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: asymptotic equality / rank
 
Normal rank
Property / Symbols used: asymptotic equality / qualifier
 
Defining formula:

∼ asymptotically-equals {\displaystyle{\displaystyle\sim}}

\asympeq
Property / Symbols used: asymptotic equality / qualifier
 
xml-id: C2.S1.E1.m2aedec
Property / Symbols used
 
Property / Symbols used: Q11492 / rank
 
Normal rank
Property / Symbols used: Q11492 / qualifier
 
Defining formula:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11492 / qualifier
 
xml-id: C11.S1.XMD3.m1ndec

Latest revision as of 15:03, 2 January 2020

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DLMF:11.11.E19
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    Statements

    Defining formula
    𝐄 ν ⁡ ( ν ) ∼ 2 1 / 3 3 7 / 6 ⁢ Γ ⁡ ( 2 3 ) ⁢ ν 1 / 3 , asymptotically-equals Weber-E 𝜈 𝜈 superscript 2 1 3 superscript 3 7 6 Euler-Gamma 2 3 superscript 𝜈 1 3 {\displaystyle{\displaystyle\mathbf{E}_{\nu}\left(\nu\right)\sim\frac{2^{1/3}}% {3^{7/6}\Gamma\left(\tfrac{2}{3}\right)\nu^{1/3}},}}
    0 references
    DLMF id
    DLMF:11.11.E19
    0 references
    constraint
    ν → + ∞ → 𝜈 {\displaystyle{\displaystyle\nu\to+\infty}}
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2abdec
    0 references
    Weber function
    Defining formula
    𝐄 ν ⁡ ( z ) Weber-E 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{E}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S10.E2.m2acdec
    0 references
    asymptotic equality
    Defining formula
    ∼ asymptotically-equals {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.E1.m2aedec
    0 references
    Q11492
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C11.S1.XMD3.m1ndec
    0 references
     
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