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DLMF:26.10.E7 - MaRDI portal

DLMF:26.10.E7 (Q8583)

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DLMF:26.10.E7
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    Statements

    DLMF 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
    Symbols used
    Q12194
    DLMF 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
    nonnegative integer
    DLMF defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C26.S1.XMD4.m1ddec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C26.S1.XMD6.m1fdec
    0 references

    Identifiers

     
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