DLMF:10.30.E5 (Q3517): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
test:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2aadec

Revision as of 12:38, 2 January 2020

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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},}}
    0 references
    DLMF id
    DLMF:10.30.E5
    0 references
    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}}
    0 references
    Symbols used
    asymptotic equality
    test
    ∼ asymptotically-equals {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.E1.m2addec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
     
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