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

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
Defining formula:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2adec
Property / Symbols used
 
Property / Symbols used: complex conjugate / rank
 
Normal rank
Property / Symbols used: complex conjugate / qualifier
 
Defining formula:

z ¯ 𝑧 {\displaystyle{\displaystyle\overline{\NVar{z}}}}

\conj{\NVar{z}}
Property / Symbols used: complex conjugate / qualifier
 
xml-id: C1.S9.E11.m2acdec
Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
Defining formula:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5aadec
Property / Symbols used
 
Property / Symbols used: Q10811 / rank
 
Normal rank
Property / Symbols used: Q10811 / qualifier
 
Defining formula:

absent {\displaystyle{\displaystyle\Re}}

\realpart@@
Property / Symbols used: Q10811 / qualifier
 
xml-id: C1.S9.E2.m1adec
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
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 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 01:29, 2 January 2020

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English
DLMF:18.19.E4
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    Statements

    h n = 2 π Γ ( n + a + a ¯ ) Γ ( n + b + b ¯ ) | Γ ( n + a + b ¯ ) | 2 ( 2 n + 2 ( a + b ) - 1 ) Γ ( n + 2 ( a + b ) - 1 ) n ! , subscript 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:18.19.E4
    0 references
    Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    C5.S2.E1.m2abdec
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2adec
    0 references
    z ¯ 𝑧 {\displaystyle{\displaystyle\overline{\NVar{z}}}}
    C1.S9.E11.m2acdec
    0 references
    ! {\displaystyle{\displaystyle!}}
    introduction.Sx4.p1.t1.r15.m5aadec
    0 references
    absent {\displaystyle{\displaystyle\Re}}
    C1.S9.E2.m1adec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C18.S1.XMD6.m1cdec
    0 references
    h n subscript 𝑛 {\displaystyle{\displaystyle h_{n}}}
    C18.S2.XMD4.m1adec
    0 references