DLMF:10.22.E47 (Q3421): Difference between revisions

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Property / constraint
 

a > 0 , b > 0 , - 1 2 < ν < 5 2 formulae-sequence 𝑎 0 formulae-sequence 𝑏 0 1 2 𝜈 5 2 {\displaystyle{\displaystyle a>0,\Re b>0,-\tfrac{1}{2}<\Re\nu<\tfrac{5}{2}}}

a>0,\realpart@@{b}>0,-\tfrac{1}{2}<\realpart@@{\nu}<\tfrac{5}{2}
Property / constraint: a > 0 , b > 0 , - 1 2 < ν < 5 2 formulae-sequence 𝑎 0 formulae-sequence 𝑏 0 1 2 𝜈 5 2 {\displaystyle{\displaystyle a>0,\Re b>0,-\tfrac{1}{2}<\Re\nu<\tfrac{5}{2}}} / rank
 
Normal rank

Revision as of 16:20, 30 December 2019

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DLMF:10.22.E47
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    Statements

    0 t ν Y ν ( a t ) t 2 + b 2 d t = - b ν - 1 K ν ( a b ) , superscript subscript 0 superscript 𝑡 𝜈 Bessel-Y-Weber 𝜈 𝑎 𝑡 superscript 𝑡 2 superscript 𝑏 2 𝑡 superscript 𝑏 𝜈 1 modified-Bessel-second-kind 𝜈 𝑎 𝑏 {\displaystyle{\displaystyle\int_{0}^{\infty}\frac{t^{\nu}Y_{\nu}\left(at% \right)}{t^{2}+b^{2}}\mathrm{d}t=-b^{\nu-1}K_{\nu}\left(ab\right),}}
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    a > 0 , b > 0 , - 1 2 < ν < 5 2 formulae-sequence 𝑎 0 formulae-sequence 𝑏 0 1 2 𝜈 5 2 {\displaystyle{\displaystyle a>0,\Re b>0,-\tfrac{1}{2}<\Re\nu<\tfrac{5}{2}}}
    0 references