DLMF:10.7.E6 (Q3059): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Bessel function of the second kind / rank
 
Normal rank
Property / Symbols used: Bessel function of the second kind / qualifier
 
test:

Y ν ⁡ ( z ) Bessel-Y-Weber 𝜈 𝑧 {\displaystyle{\displaystyle Y_{\NVar{\nu}}\left(\NVar{z}\right)}}

\BesselY{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: Bessel function of the second kind / qualifier
 
xml-id: C10.S2.E3.m2acdec

Revision as of 14:09, 2 January 2020

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DLMF:10.7.E6
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    Statements

    test
    Y i ⁢ ν ⁡ ( z ) = i ⁢ csch ⁡ ( ν ⁢ π ) Γ ⁡ ( 1 - i ⁢ ν ) ⁢ ( 1 2 ⁢ z ) - i ⁢ ν - i ⁢ coth ⁡ ( ν ⁢ π ) Γ ⁡ ( 1 + i ⁢ ν ) ⁢ ( 1 2 ⁢ z ) i ⁢ ν + e | ν ⁢ ph ⁡ z | ⁢ o ⁡ ( 1 ) , Bessel-Y-Weber 𝑖 𝜈 𝑧 𝑖 𝜈 𝜋 Euler-Gamma 1 𝑖 𝜈 superscript 1 2 𝑧 𝑖 𝜈 𝑖 hyperbolic-cotangent 𝜈 𝜋 Euler-Gamma 1 𝑖 𝜈 superscript 1 2 𝑧 𝑖 𝜈 superscript 𝑒 𝜈 phase 𝑧 little-o 1 {\displaystyle{\displaystyle Y_{i\nu}\left(z\right)=\frac{i\operatorname{csch}% \left(\nu\pi\right)}{\Gamma\left(1-i\nu\right)}(\tfrac{1}{2}z)^{-i\nu}-\frac{i% \coth\left(\nu\pi\right)}{\Gamma\left(1+i\nu\right)}(\tfrac{1}{2}z)^{i\nu}+e^{% |\nu\operatorname{ph}z|}o\left(1\right),}}
    0 references
    DLMF id
    DLMF:10.7.E6
    0 references
    constraint
    ν ∈ ℝ 𝜈 {\displaystyle{\displaystyle\nu\in\mathbb{R}}}
    0 references
    ν ∈ ℝ 𝜈 ℝ {\displaystyle{\displaystyle\nu\in\mathbb{R}}}
    0 references
    ν ≠ 0 𝜈 0 {\displaystyle{\displaystyle\nu\neq 0}}
    0 references
    Symbols used
    Bessel function of the second kind
    test
    Y ν ⁡ ( z ) Bessel-Y-Weber 𝜈 𝑧 {\displaystyle{\displaystyle Y_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E3.m2acdec
    0 references
     
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