DLMF:26.12.E23 (Q7940): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12207 / rank
 
Normal rank
Property / Symbols used: Q12207 / qualifier
 
test:

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.m1ddec

Revision as of 13:06, 2 January 2020

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DLMF:26.12.E23
No description defined

    Statements

    test
    ∑ π ⊆ B ⁢ ( r , r , r ) π ⁢  cyclically symmetric q | π | = ∏ h = 1 r 1 - q 3 ⁢ h - 1 1 - q 3 ⁢ h - 2 ⁢ ∏ 1 ≤ h < j ≤ r 1 - q 3 ⁢ ( h + 2 ⁢ j - 1 ) 1 - q 3 ⁢ ( h + j - 1 ) = ∏ h = 1 r ( 1 - q 3 ⁢ h - 1 1 - q 3 ⁢ h - 2 ⁢ ∏ j = h r 1 - q 3 ⁢ ( r + h + j - 1 ) 1 - q 3 ⁢ ( 2 ⁢ h + j - 1 ) ) . subscript 𝜋 𝐵 𝑟 𝑟 𝑟 𝜋  cyclically symmetric superscript 𝑞 𝜋 superscript subscript product ℎ 1 𝑟 1 superscript 𝑞 3 ℎ 1 1 superscript 𝑞 3 ℎ 2 subscript product 1 ℎ 𝑗 𝑟 1 superscript 𝑞 3 ℎ 2 𝑗 1 1 superscript 𝑞 3 ℎ 𝑗 1 superscript subscript product ℎ 1 𝑟 1 superscript 𝑞 3 ℎ 1 1 superscript 𝑞 3 ℎ 2 superscript subscript product 𝑗 ℎ 𝑟 1 superscript 𝑞 3 𝑟 ℎ 𝑗 1 1 superscript 𝑞 3 2 ℎ 𝑗 1 {\displaystyle{\displaystyle\sum_{\begin{subarray}{c}\pi\subseteq B(r,r,r)\\ \pi\mbox{\scriptsize\ cyclically symmetric}\end{subarray}}q^{\left|\pi\right|}% =\prod_{h=1}^{r}\frac{1-q^{3h-1}}{1-q^{3h-2}}\prod_{1\leq h<j\leq r}\frac{1-q^% {3(h+2j-1)}}{1-q^{3(h+j-1)}}=\prod_{h=1}^{r}\left(\frac{1-q^{3h-1}}{1-q^{3h-2}% }\prod_{j=h}^{r}\frac{1-q^{3(r+h+j-1)}}{1-q^{3(2h+j-1)}}\right).}}
    0 references
    DLMF id
    DLMF:26.12.E23
    0 references
    Symbols used
    Q12209
    test
    ⊆ {\displaystyle{\displaystyle\subseteq}}
    xml-id
    introduction.Sx4.p2.t1.r3.m2acdec
    0 references
    Q12186
    test
    h ℎ {\displaystyle{\displaystyle h}}
    xml-id
    C26.S1.XMD2.m1bdec
    0 references
    Q12176
    test
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C26.S1.XMD3.m1bdec
    0 references
    Q12210
    test
    π 𝜋 {\displaystyle{\displaystyle\pi}}
    xml-id
    C26.S12.XMD1.m1cdec
    0 references
    Q12201
    test
    r 𝑟 {\displaystyle{\displaystyle r}}
    xml-id
    C26.S12.XMD2.m1rdec
    0 references
    Q12207
    test
    B ⁢ ( r , s , t ) 𝐵 𝑟 𝑠 𝑡 {\displaystyle{\displaystyle B(r,s,t)}}
    xml-id
    C26.S12.XMD8.m1ddec
    0 references
     
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