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Formula:3682

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Digital Library of Mathematical Functions ID 9.13.E21

U 2 ⁢ ( x , α ) = ( α + 2 ) 1 / ( α + 2 ) ⁢ Γ ⁡ ( α + 3 α + 2 ) ⁢ x 1 / 2 ⁢ J 1 / ( α + 2 ) ⁡ ( 2 α + 2 ⁢ x ( α + 2 ) / 2 ) , subscript 𝑈 2 𝑥 𝛼 superscript 𝛼 2 1 𝛼 2 Euler-Gamma 𝛼 3 𝛼 2 superscript 𝑥 1 2 Bessel-J 1 𝛼 2 2 𝛼 2 superscript 𝑥 𝛼 2 2 {\displaystyle{\displaystyle U_{2}(x,\alpha)=(\alpha+2)^{1/(\alpha+2)}\*\Gamma% \left(\frac{\alpha+3}{\alpha+2}\right)x^{1/2}J_{1/(\alpha+2)}\left(\frac{2}{% \alpha+2}x^{(\alpha+2)/2}\right),}}


Constraint(s)

Symbols List

  • J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}} : Bessel function of the first kind
  • Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}} : gamma function
  • α 𝛼 {\displaystyle{\displaystyle\alpha}} : parameter (locally)
  • x 𝑥 {\displaystyle{\displaystyle x}} : parameter (locally)
  • U i subscript 𝑈 𝑖 {\displaystyle{\displaystyle U_{i}}} : Smirnov’s generalized Airy function
  •  Edit this on Wikidata

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This page was last edited on 3 March 2024, at 01:53.
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