DLMF:5.5.E7 (Q2065)

From DRMF
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:5.5.E7
No description defined

    Statements

    Defining formula
    ∏ 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}.}}
    0 references
    DLMF id
    DLMF:5.5.E7
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2addec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
    0 references
    Q11274
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C5.S1.XMD3.m1adec
    0 references
    Q11279
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C5.S1.XMD4.m1adec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q2065&oldid=28581"