DLMF:26.10.E7 (Q7890): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q12174 / rank
 
Normal rank
Property / Symbols used: Q12174 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q12174 / qualifier
 
xml-id: C26.S1.XMD4.m1ddec

Revision as of 14:00, 2 January 2020

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DLMF:26.10.E7
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    Statements

    Defining formula
    ∑ ( - 1 ) k ⁢ p ⁡ ( 𝒟 , n - 1 2 ⁢ ( 3 ⁢ k 2 ± k ) ) = { ( - 1 ) r , n = 3 ⁢ r 2 ± r , 0 , otherwise , superscript 1 𝑘 restricted-partitions-P 𝒟 𝑛 1 2 plus-or-minus 3 superscript 𝑘 2 𝑘 cases superscript 1 𝑟 𝑛 plus-or-minus 3 superscript 𝑟 2 𝑟 0 otherwise {\displaystyle{\displaystyle\sum(-1)^{k}p\left(\mathcal{D},n-\tfrac{1}{2}(3k^{% 2}\pm k)\right)=\begin{cases}(-1)^{r},&n=3r^{2}\pm r,\\ 0,&\mbox{otherwise},\end{cases}}}
    0 references
    DLMF id
    DLMF:26.10.E7
    0 references
    Symbols used
    Q12191
    Defining formula
    p ⁡ ( condition , n ) restricted-partitions-P condition 𝑛 {\displaystyle{\displaystyle p\left(\NVar{\mathrm{condition}},\NVar{n}\right)}}
    xml-id
    C26.S10.SS1.m4afdec
    0 references
    Q12174
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C26.S1.XMD4.m1ddec
    0 references
     
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