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Formula:2611

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Digital Library of Mathematical Functions ID 5.5.E7

∏ k = 1 n - 1 Γ ⁡ ( k n ) = ( 2 ⁢ π ) ( n - 1 ) / 2 ⁢ n - 1 / 2 . superscript subscript product 𝑘 1 𝑛 1 Euler-Gamma 𝑘 𝑛 superscript 2 𝜋 𝑛 1 2 superscript 𝑛 1 2 {\displaystyle{\displaystyle\prod_{k=1}^{n-1}\Gamma\left(\frac{k}{n}\right)=(2% \pi)^{(n-1)/2}n^{-1/2}.}}


Constraint(s)

Symbols List

  • 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
  • n 𝑛 {\displaystyle{\displaystyle n}} : nonnegative integer
  • k 𝑘 {\displaystyle{\displaystyle k}} : nonnegative integer
  •  Edit this on Wikidata

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This page was last edited on 28 January 2024, at 10:30.
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