DLMF:26.12.E21 (Q7938): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12203 / rank
 
Normal rank
Property / Symbols used: Q12203 / qualifier
 
Defining formula:

t 𝑡 {\displaystyle{\displaystyle t}}

t
Property / Symbols used: Q12203 / qualifier
 
xml-id: C26.S12.XMD4.m1idec
Property / Symbols used
 
Property / Symbols used: Q12207 / rank
 
Normal rank
Property / Symbols used: Q12207 / qualifier
 
Defining formula:

B ⁢ ( r , s , t ) 𝐵 𝑟 𝑠 𝑡 {\displaystyle{\displaystyle B(r,s,t)}}

B(r,s,t)
Property / Symbols used: Q12207 / qualifier
 
xml-id: C26.S12.XMD8.m1bdec
Property / Symbols used
 
Property / Symbols used: Q12189 / rank
 
Normal rank
Property / Symbols used: Q12189 / qualifier
 
Defining formula:

q 𝑞 {\displaystyle{\displaystyle q}}

q
Property / Symbols used: Q12189 / qualifier
 
xml-id: C26.S9.XMD1.m1adec

Latest revision as of 14:06, 2 January 2020

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DLMF:26.12.E21
No description defined

    Statements

    Defining formula
    ∑ π ⊆ B ⁢ ( r , s , t ) q | π | = ∏ ( h , j , k ) ∈ B ⁢ ( r , s , t ) 1 - q h + j + k - 1 1 - q h + j + k - 2 = ∏ h = 1 r ∏ j = 1 s 1 - q h + j + t - 1 1 - q h + j - 1 , subscript 𝜋 𝐵 𝑟 𝑠 𝑡 superscript 𝑞 𝜋 subscript product ℎ 𝑗 𝑘 𝐵 𝑟 𝑠 𝑡 1 superscript 𝑞 ℎ 𝑗 𝑘 1 1 superscript 𝑞 ℎ 𝑗 𝑘 2 superscript subscript product ℎ 1 𝑟 superscript subscript product 𝑗 1 𝑠 1 superscript 𝑞 ℎ 𝑗 𝑡 1 1 superscript 𝑞 ℎ 𝑗 1 {\displaystyle{\displaystyle\sum_{\pi\subseteq B(r,s,t)}q^{|\pi|}=\prod_{(h,j,% k)\in B(r,s,t)}\frac{1-q^{h+j+k-1}}{1-q^{h+j+k-2}}=\prod_{h=1}^{r}\prod_{j=1}^% {s}\frac{1-q^{h+j+t-1}}{1-q^{h+j-1}},}}
    0 references
    DLMF id
    DLMF:26.12.E21
    0 references
    comment
    Warning: Falling back to standard tex;
    0 references
    Symbols used
    Q10784
    Defining formula
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2aadec
    0 references
    Q12209
    Defining formula
    ⊆ {\displaystyle{\displaystyle\subseteq}}
    xml-id
    introduction.Sx4.p2.t1.r3.m2aadec
    0 references
    Q12186
    Defining formula
    h ℎ {\displaystyle{\displaystyle h}}
    xml-id
    C26.S1.XMD2.m1dec
    0 references
    Q12176
    Defining formula
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C26.S1.XMD3.m1dec
    0 references
    Q12174
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C26.S1.XMD4.m1adec
    0 references
    Q12210
    Defining formula
    π 𝜋 {\displaystyle{\displaystyle\pi}}
    xml-id
    C26.S12.XMD1.m1adec
    0 references
    Q12201
    Defining formula
    r 𝑟 {\displaystyle{\displaystyle r}}
    xml-id
    C26.S12.XMD2.m1pdec
    0 references
    Q12202
    Defining formula
    s 𝑠 {\displaystyle{\displaystyle s}}
    xml-id
    C26.S12.XMD3.m1edec
    0 references
    Q12203
    Defining formula
    t 𝑡 {\displaystyle{\displaystyle t}}
    xml-id
    C26.S12.XMD4.m1idec
    0 references
    Q12207
    Defining formula
    B ⁢ ( r , s , t ) 𝐵 𝑟 𝑠 𝑡 {\displaystyle{\displaystyle B(r,s,t)}}
    xml-id
    C26.S12.XMD8.m1bdec
    0 references
    Q12189
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C26.S9.XMD1.m1adec
    0 references
     
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