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DLMF:24.19.E1 - MaRDI portal

DLMF:24.19.E1 (Q8285)

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DLMF:24.19.E1
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    Statements

    DLMF defining formula
    N 2 ⁢ n = 2 ⁢ ( 2 ⁢ n ) ! ( 2 ⁢ π ) 2 ⁢ n ⁢ ( ∏ p - 1 | 2 ⁢ n p ) ⁢ ( ∏ p p 2 ⁢ n p 2 ⁢ n - 1 ) , subscript 𝑁 2 𝑛 2 2 𝑛 superscript 2 𝜋 2 𝑛 subscript product 𝑝 divides 1 2 𝑛 𝑝 subscript product 𝑝 superscript 𝑝 2 𝑛 superscript 𝑝 2 𝑛 1 {\displaystyle{\displaystyle N_{2n}=\frac{2(2n)!}{(2\pi)^{2n}}\left(\prod_{p-1% \mathbin{|}2n}p\right)\left(\prod_{p}\frac{p^{2n}}{p^{2n}-1}\right),}}
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
    0 references
    Q10729
    DLMF defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
    0 references
    integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1dec
    0 references
    prime
    DLMF defining formula
    p 𝑝 {\displaystyle{\displaystyle p}}
    xml-id
    C24.S1.XMD8.m1dec
    0 references
     
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