DLMF:11.11.E18 (Q4781): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: real or complex order / rank
 
Normal rank
Property / Symbols used: real or complex order / qualifier
 
DLMF defining formula:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: real or complex order / qualifier
 
xml-id: C11.S1.XMD3.m1mdec

Revision as of 17:40, 21 December 2021

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DLMF:11.11.E18
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    Statements

    DLMF defining formula
    𝐉 ν ⁡ ( ν ) ∼ 2 1 / 3 3 2 / 3 ⁢ Γ ⁡ ( 2 3 ) ⁢ ν 1 / 3 , asymptotically-equals Anger-J 𝜈 𝜈 superscript 2 1 3 superscript 3 2 3 Euler-Gamma 2 3 superscript 𝜈 1 3 {\displaystyle{\displaystyle\mathbf{J}_{\nu}\left(\nu\right)\sim\frac{2^{1/3}}% {3^{2/3}\Gamma\left(\tfrac{2}{3}\right)\nu^{1/3}},}}
    0 references
    constraint
    ν → + ∞ → 𝜈 {\displaystyle{\displaystyle\nu\to+\infty}}
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    Symbols used
    Anger function
    DLMF defining formula
    𝐉 ν ⁡ ( z ) Anger-J 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{J}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S10.E1.m2abdec
    0 references
    gamma function
    DLMF defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aadec
    0 references
    asymptotic equality
    DLMF defining formula
    ∼ asymptotically-equals {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.E1.m2addec
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    real or complex order
    DLMF defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C11.S1.XMD3.m1mdec
    0 references

    Identifiers

     
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