DLMF:10.41.E1 (Q3593)

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DLMF:10.41.E1
No description defined

    Statements

    Defining formula
    I ν ⁡ ( z ) ∼ 1 2 ⁢ π ⁢ ν ⁢ ( e ⁢ z 2 ⁢ ν ) ν , asymptotically-equals modified-Bessel-first-kind 𝜈 𝑧 1 2 𝜋 𝜈 superscript 𝑒 𝑧 2 𝜈 𝜈 {\displaystyle{\displaystyle I_{\nu}\left(z\right)\sim\frac{1}{\sqrt{2\pi\nu}}% \left(\frac{ez}{2\nu}\right)^{\nu},}}
    0 references
    DLMF id
    DLMF:10.41.E1
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    Symbols used
    asymptotic equality
    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
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
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    modified Bessel function of the first kind
    Defining formula
    I ν ⁡ ( z ) modified-Bessel-first-kind 𝜈 𝑧 {\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S25.E2.m2adec
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    Q11426
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1dec
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    Q11427
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1dec
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