DLMF:18.25.E12 (Q5927): Difference between revisions

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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.m1hdec
Property / Symbols used
 
Property / Symbols used: Q11736 / rank
 
Normal rank
Property / Symbols used: Q11736 / qualifier
 
Defining formula:

N 𝑁 {\displaystyle{\displaystyle N}}

N
Property / Symbols used: Q11736 / qualifier
 
xml-id: C18.S1.XMD7.m1ddec
Property / Symbols used
 
Property / Symbols used: Q11754 / rank
 
Normal rank
Property / Symbols used: Q11754 / qualifier
 
Defining formula:

δ 𝛿 {\displaystyle{\displaystyle\delta}}

\delta
Property / Symbols used: Q11754 / qualifier
 
xml-id: C18.S1.XMD8.m1edec
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.m1ddec

Latest revision as of 01:42, 2 January 2020

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DLMF:18.25.E12
No description defined

    Statements

    Defining formula
    h n = ( - β ) N ⁢ ( γ + δ + 2 ) N ( - β + γ + 1 ) N ⁢ ( δ + 1 ) N ⁢ ( n + α + β + 1 ) n ⁢ n ! ( α + β + 2 ) 2 ⁢ n ⁢ ( α + β - γ + 1 ) n ⁢ ( α - δ + 1 ) n ⁢ ( β + 1 ) n ( α + 1 ) n ⁢ ( β + δ + 1 ) n ⁢ ( γ + 1 ) n . subscript ℎ 𝑛 Pochhammer 𝛽 𝑁 Pochhammer 𝛾 𝛿 2 𝑁 Pochhammer 𝛽 𝛾 1 𝑁 Pochhammer 𝛿 1 𝑁 Pochhammer 𝑛 𝛼 𝛽 1 𝑛 𝑛 Pochhammer 𝛼 𝛽 2 2 𝑛 Pochhammer 𝛼 𝛽 𝛾 1 𝑛 Pochhammer 𝛼 𝛿 1 𝑛 Pochhammer 𝛽 1 𝑛 Pochhammer 𝛼 1 𝑛 Pochhammer 𝛽 𝛿 1 𝑛 Pochhammer 𝛾 1 𝑛 {\displaystyle{\displaystyle h_{n}=\frac{{\left(-\beta\right)_{N}}{\left(% \gamma+\delta+2\right)_{N}}}{{\left(-\beta+\gamma+1\right)_{N}}{\left(\delta+1% \right)_{N}}}\frac{{\left(n+\alpha+\beta+1\right)_{n}}n!}{{\left(\alpha+\beta+% 2\right)_{2n}}}\*\frac{{\left(\alpha+\beta-\gamma+1\right)_{n}}{\left(\alpha-% \delta+1\right)_{n}}{\left(\beta+1\right)_{n}}}{{\left(\alpha+1\right)_{n}}{% \left(\beta+\delta+1\right)_{n}}{\left(\gamma+1\right)_{n}}}.}}
    0 references
    DLMF id
    DLMF:18.25.E12
    0 references
    Symbols used
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1aadec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5acdec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1hdec
    0 references
    Q11736
    Defining formula
    N 𝑁 {\displaystyle{\displaystyle N}}
    xml-id
    C18.S1.XMD7.m1ddec
    0 references
    Q11754
    Defining formula
    δ 𝛿 {\displaystyle{\displaystyle\delta}}
    xml-id
    C18.S1.XMD8.m1edec
    0 references
    DLMF:18.2.E5
    Defining formula
    h n subscript ℎ 𝑛 {\displaystyle{\displaystyle h_{n}}}
    xml-id
    C18.S2.XMD4.m1ddec
    0 references
     
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