DLMF:10.27.E10 (Q3500): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
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
 
Defining formula:

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.m2afdec

Revision as of 13:37, 2 January 2020

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DLMF:10.27.E10
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    Statements

    Defining formula
    - π ⁢ Y ν ⁡ ( z ) = e - ν ⁢ π ⁢ i / 2 ⁢ K ν ⁡ ( z ⁢ e - π ⁢ i / 2 ) + e ν ⁢ π ⁢ i / 2 ⁢ K ν ⁡ ( z ⁢ e π ⁢ i / 2 ) , 𝜋 Bessel-Y-Weber 𝜈 𝑧 superscript 𝑒 𝜈 𝜋 𝑖 2 modified-Bessel-second-kind 𝜈 𝑧 superscript 𝑒 𝜋 𝑖 2 superscript 𝑒 𝜈 𝜋 𝑖 2 modified-Bessel-second-kind 𝜈 𝑧 superscript 𝑒 𝜋 𝑖 2 {\displaystyle{\displaystyle-\pi Y_{\nu}\left(z\right)=e^{-\nu\pi i/2}K_{\nu}% \left(ze^{-\pi i/2}\right)+e^{\nu\pi i/2}K_{\nu}\left(ze^{\pi i/2}\right),}}
    0 references
    DLMF id
    DLMF:10.27.E10
    0 references
    constraint
    | ph ⁡ z | ≤ 1 2 ⁢ π phase 𝑧 1 2 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{1}{2}\pi}}
    0 references
    Symbols used
    Bessel function of the second kind
    Defining formula
    Y ν ⁡ ( z ) Bessel-Y-Weber 𝜈 𝑧 {\displaystyle{\displaystyle Y_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E3.m2adec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2afdec
    0 references
     
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