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DLMF:18.25.E8 - MaRDI portal

DLMF:18.25.E8 (Q6619)

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DLMF:18.25.E8
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    Statements

    DLMF defining formula
    h n = n ! ⁢  2 ⁢ π ⁢ ∏ j < ℓ Γ ⁡ ( n + a j + a ℓ ) . subscript ℎ 𝑛 𝑛  2 𝜋 subscript product 𝑗 ℓ Euler-Gamma 𝑛 subscript 𝑎 𝑗 subscript 𝑎 ℓ {\displaystyle{\displaystyle h_{n}=n!\,2\pi\prod_{j<\ell}\Gamma\left(n+a_{j}+a% _{\ell}\right).}}
    0 references
    Symbols used
    gamma function
    DLMF defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2acdec
    0 references
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    Q10729
    DLMF defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
    0 references
    nonnegative integer
    DLMF defining formula
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C18.S1.XMD4.m1adec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1edec
    0 references
    18.2.E5
    DLMF defining formula
    h n subscript ℎ 𝑛 {\displaystyle{\displaystyle h_{n}}}
    xml-id
    C18.S2.XMD4.m1bdec
    0 references

    Identifiers

     
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