DLMF:18.19.E4 (Q5834): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11726 / rank
 
Normal rank
Property / Symbols used: Q11726 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11726 / qualifier
 
xml-id: C18.S1.XMD6.m1cdec

Revision as of 01:29, 2 January 2020

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DLMF:18.19.E4
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    Statements

    Defining formula
    h n = 2 ⁢ π ⁢ Γ ⁡ ( n + a + a ¯ ) ⁢ Γ ⁡ ( n + b + b ¯ ) ⁢ | Γ ⁡ ( n + a + b ¯ ) | 2 ( 2 ⁢ n + 2 ⁢ ℜ ⁡ ( a + b ) - 1 ) ⁢ Γ ⁡ ( n + 2 ⁢ ℜ ⁡ ( a + b ) - 1 ) ⁢ n ! , subscript ℎ 𝑛 2 𝜋 Euler-Gamma 𝑛 𝑎 𝑎 Euler-Gamma 𝑛 𝑏 𝑏 superscript Euler-Gamma 𝑛 𝑎 𝑏 2 2 𝑛 2 𝑎 𝑏 1 Euler-Gamma 𝑛 2 𝑎 𝑏 1 𝑛 {\displaystyle{\displaystyle h_{n}=\frac{2\pi\Gamma\left(n+a+\overline{a}% \right)\Gamma\left(n+b+\overline{b}\right)|\Gamma\left(n+a+\overline{b}\right)% |^{2}}{\left(2n+2\Re(a+b)-1\right)\Gamma\left(n+2\Re(a+b)-1\right)n!},}}
    0 references
    DLMF id
    DLMF:18.19.E4
    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.m2abdec
    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
    complex conjugate
    Defining formula
    z ¯ 𝑧 {\displaystyle{\displaystyle\overline{\NVar{z}}}}
    xml-id
    C1.S9.E11.m2acdec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
    0 references
    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1adec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1cdec
    0 references
     
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