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DLMF:9.11.E16

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Formula:3621
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MaRDI QIDQ3621

  • Label: DLMF:9.11.E16


Digital Library of Mathematical Functions ID 9.11.E16

∫ - ∞ ∞ Ai 3 ⁡ ( t ) ⁢ d t = Γ 2 ⁡ ( 1 3 ) 4 ⁢ π 2 , superscript subscript Airy-Ai 3 𝑡 𝑡 Euler-Gamma 2 1 3 4 superscript 𝜋 2 {\displaystyle{\displaystyle\int_{-\infty}^{\infty}{\mathrm{Ai}^{3}}\left(t% \right)\mathrm{d}t=\frac{{\Gamma^{2}}\left(\frac{1}{3}\right)}{4\pi^{2}},}}


Constraint(s)

Symbols List

  • Ai ⁡ ( z ) Airy-Ai 𝑧 {\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}} :
  • Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}} : gamma function
  • π {\displaystyle{\displaystyle\pi}} : the ratio of the circumference of a circle to its diameter
  • d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}} : differential of x
  • ∫ {\displaystyle{\displaystyle\int}} : integral
  •  Edit this on Wikidata

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