DLMF:18.25.E5 (Q5920): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: DLMF:18.2.E5 / rank
 
Normal rank
Property / Symbols used: DLMF:18.2.E5 / qualifier
 
Defining formula:

h n subscript ℎ 𝑛 {\displaystyle{\displaystyle h_{n}}}

h_{n}
Property / Symbols used: DLMF:18.2.E5 / qualifier
 
xml-id: C18.S2.XMD4.m1adec

Latest revision as of 01:41, 2 January 2020

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DLMF:18.25.E5
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    Statements

    Defining formula
    h n = n ! ⁢  2 ⁢ π ⁢ ∏ j < ℓ Γ ⁡ ( n + a j + a ℓ ) ( 2 ⁢ n - 1 + ∑ j a j ) ⁢ Γ ⁡ ( n - 1 + ∑ j a j ) . subscript ℎ 𝑛 𝑛  2 𝜋 subscript product 𝑗 ℓ Euler-Gamma 𝑛 subscript 𝑎 𝑗 subscript 𝑎 ℓ 2 𝑛 1 subscript 𝑗 subscript 𝑎 𝑗 Euler-Gamma 𝑛 1 subscript 𝑗 subscript 𝑎 𝑗 {\displaystyle{\displaystyle h_{n}=\frac{n!\,2\pi\prod_{j<\ell}\Gamma\left(n+a% _{j}+a_{\ell}\right)}{(2n-1+\sum_{j}a_{j})\Gamma\left(n-1+\sum_{j}a_{j}\right)% }.}}
    0 references
    DLMF id
    DLMF:18.25.E5
    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.m2aadec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
    0 references
    Q11744
    Defining formula
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C18.S1.XMD4.m1dec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1cdec
    0 references
    DLMF:18.2.E5
    Defining formula
    h n subscript ℎ 𝑛 {\displaystyle{\displaystyle h_{n}}}
    xml-id
    C18.S2.XMD4.m1adec
    0 references
     
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