DLMF:10.9#Ex6 (Q3080): Difference between revisions

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Property / constraint
 

x > 0 𝑥 0 {\displaystyle{\displaystyle x>0}}

x>0
Property / constraint: x > 0 𝑥 0 {\displaystyle{\displaystyle x>0}} / rank
 
Normal rank

Latest revision as of 17:16, 30 December 2019

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DLMF:10.9#Ex6
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    Statements

    Defining formula
    Y ν ⁡ ( x ) = - 2 ⁢ ( 1 2 ⁢ x ) - ν π 1 2 ⁢ Γ ⁡ ( 1 2 - ν ) ⁢ ∫ 1 ∞ cos ⁡ ( x ⁢ t ) ⁢ d t ( t 2 - 1 ) ν + 1 2 , Bessel-Y-Weber 𝜈 𝑥 2 superscript 1 2 𝑥 𝜈 superscript 𝜋 1 2 Euler-Gamma 1 2 𝜈 superscript subscript 1 𝑥 𝑡 𝑡 superscript superscript 𝑡 2 1 𝜈 1 2 {\displaystyle{\displaystyle Y_{\nu}\left(x\right)=-\frac{2(\tfrac{1}{2}x)^{-% \nu}}{\pi^{\frac{1}{2}}\Gamma\left(\tfrac{1}{2}-\nu\right)}\int_{1}^{\infty}% \frac{\cos\left(xt\right)\mathrm{d}t}{(t^{2}-1)^{\nu+\frac{1}{2}}},}}
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    DLMF id
    DLMF:10.9#Ex6
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    constraint
    | ℜ ⁡ ν | < 1 2 𝜈 1 2 {\displaystyle{\displaystyle|\Re\nu|<\tfrac{1}{2}}}
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    | ℜ ⁡ ν | < 1 2 𝜈 1 2 {\displaystyle{\displaystyle|\Re\nu|<\tfrac{1}{2}}}
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    x > 0 𝑥 0 {\displaystyle{\displaystyle x>0}}
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