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DLMF:10.19.E1 - MaRDI portal

DLMF:10.19.E1 (Q3913)

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DLMF:10.19.E1
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    Statements

    DLMF defining formula
    J ν ⁡ ( z ) ∼ 1 2 ⁢ π ⁢ ν ⁢ ( e ⁢ z 2 ⁢ ν ) ν , asymptotically-equals Bessel-J 𝜈 𝑧 1 2 𝜋 𝜈 superscript 𝑒 𝑧 2 𝜈 𝜈 {\displaystyle{\displaystyle J_{\nu}\left(z\right)\sim\frac{1}{\sqrt{2\pi\nu}}% \left(\frac{ez}{2\nu}\right)^{\nu},}}
    0 references
    Symbols used
    Bessel function of the first kind
    DLMF defining formula
    J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E2.m2adec
    0 references
    asymptotic equality
    DLMF defining formula
    ∼ asymptotically-equals {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.E1.m2adec
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    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
    0 references
    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
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    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1dec
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    complex parameter
    DLMF defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1dec
    0 references

    Identifiers

     
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