DLMF:10.30.E5 (Q3517)

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DLMF:10.30.E5
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    Statements

    test
    I ν ⁡ ( z ) ∼ e ± ( ν + 1 2 ) ⁢ π ⁢ i ⁢ e - z / 2 ⁢ π ⁢ z , asymptotically-equals modified-Bessel-first-kind 𝜈 𝑧 superscript 𝑒 plus-or-minus 𝜈 1 2 𝜋 𝑖 superscript 𝑒 𝑧 2 𝜋 𝑧 {\displaystyle{\displaystyle I_{\nu}\left(z\right)\sim e^{\pm(\nu+\frac{1}{2})% \pi i}e^{-z}/\sqrt{2\pi z},}}
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    DLMF id
    DLMF:10.30.E5
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    constraint
    1 2 ⁢ π + δ ≤ ± ph ⁡ z ≤ 3 2 ⁢ π - δ 1 2 𝜋 𝛿 plus-or-minus phase 𝑧 3 2 𝜋 𝛿 {\displaystyle{\displaystyle\tfrac{1}{2}\pi+\delta\leq\pm\operatorname{ph}z% \leq\tfrac{3}{2}\pi-\delta}}
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    Symbols used
    asymptotic equality
    test
    ∼ asymptotically-equals {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.E1.m2addec
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    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
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    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
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    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
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    modified Bessel function of the first kind
    test
    I ν ⁡ ( z ) modified-Bessel-first-kind 𝜈 𝑧 {\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S25.E2.m2abdec
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    Q10817
    test
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1aadec
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    Q11426
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1ddec
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    Q11427
    test
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1cdec
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