DLMF:10.41.E3 (Q3595)

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DLMF:10.41.E3
No description defined

    Statements

    Defining formula
    I ν ⁡ ( ν ⁢ z ) ∼ e ν ⁢ η ( 2 ⁢ π ⁢ ν ) 1 2 ⁢ ( 1 + z 2 ) 1 4 ⁢ ∑ k = 0 ∞ U k ⁢ ( p ) ν k , asymptotic-expansion modified-Bessel-first-kind 𝜈 𝜈 𝑧 superscript 𝑒 𝜈 𝜂 superscript 2 𝜋 𝜈 1 2 superscript 1 superscript 𝑧 2 1 4 superscript subscript 𝑘 0 subscript 𝑈 𝑘 𝑝 superscript 𝜈 𝑘 {\displaystyle{\displaystyle I_{\nu}\left(\nu z\right)\sim\frac{e^{\nu\eta}}{(% 2\pi\nu)^{\frac{1}{2}}(1+z^{2})^{\frac{1}{4}}}\sum_{k=0}^{\infty}\frac{U_{k}(p% )}{\nu^{k}},}}
    0 references
    DLMF id
    DLMF:10.41.E3
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    Symbols used
    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11adec
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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.m2abdec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
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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.m2aadec
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    Q11428
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C10.S1.XMD3.m1dec
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    Q11426
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1bdec
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    Q11427
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1bdec
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    DLMF:10.41.E7
    Defining formula
    η 𝜂 {\displaystyle{\displaystyle\eta}}
    xml-id
    C10.S41.XMD1.m1dec
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    Q11453
    Defining formula
    U k ⁢ ( p ) subscript 𝑈 𝑘 𝑝 {\displaystyle{\displaystyle U_{k}(p)}}
    xml-id
    C10.S41.XMD3.m1dec
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