DLMF:10.7.E5 (Q3058): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11426 / rank
 
Normal rank
Property / Symbols used: Q11426 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11426 / qualifier
 
xml-id: C10.S1.XMD6.m1ddec

Revision as of 15:09, 2 January 2020

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DLMF:10.7.E5
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    Statements

    Defining formula
    Y - ν ⁡ ( z ) ∼ - ( 1 / π ) ⁢ cos ⁡ ( ν ⁢ π ) ⁢ Γ ⁡ ( ν ) ⁢ ( 1 2 ⁢ z ) - ν , asymptotically-equals Bessel-Y-Weber 𝜈 𝑧 1 𝜋 𝜈 𝜋 Euler-Gamma 𝜈 superscript 1 2 𝑧 𝜈 {\displaystyle{\displaystyle Y_{-\nu}\left(z\right)\sim-(1/\pi)\cos\left(\nu% \pi\right)\Gamma\left(\nu\right)(\tfrac{1}{2}z)^{-\nu},}}
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    DLMF id
    DLMF:10.7.E5
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    constraint
    ℜ ⁡ ν > 0 𝜈 0 {\displaystyle{\displaystyle\Re\nu>0}}
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    ℜ ⁡ ν > 0 𝜈 0 {\displaystyle{\displaystyle\Re\nu>0}}
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    ν ≠ 1 2 , 3 2 , 5 2 , … 𝜈 1 2 3 2 5 2 … {\displaystyle{\displaystyle\nu\neq\tfrac{1}{2},\tfrac{3}{2},\tfrac{5}{2},% \ldots}}
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    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.m2abdec
    0 references
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2abdec
    0 references
    asymptotic equality
    Defining formula
    ∼ asymptotically-equals {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.E1.m2addec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
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    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2adec
    0 references
    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1aadec
    0 references
    Q11426
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1ddec
    0 references
     
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