DLMF:26.9.E6 (Q7879)

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DLMF:26.9.E6
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    Statements

    Defining formula
    ∑ n = 0 ∞ p k ⁡ ( ≤ m , n ) ⁢ q n = [ m + k k ] q . superscript subscript 𝑛 0 restricted-partitions-P-at-most 𝑘 absent 𝑚 𝑛 superscript 𝑞 𝑛 q-binomial 𝑚 𝑘 𝑘 𝑞 {\displaystyle{\displaystyle\sum_{n=0}^{\infty}p_{k}\left(\leq m,n\right)q^{n}% =\genfrac{[}{]}{0.0pt}{}{m+k}{k}_{q}.}}
    0 references
    DLMF id
    DLMF:26.9.E6
    0 references
    Symbols used
    $$q$$ -binomial coefficient (or Gaussian polynomial)
    Defining formula
    [ n m ] q q-binomial 𝑛 𝑚 𝑞 {\displaystyle{\displaystyle\genfrac{[}{]}{0.0pt}{}{\NVar{n}}{\NVar{m}}_{\NVar% {q}}}}
    xml-id
    C17.S2.E27.m2abdec
    0 references
    Q12190
    Defining formula
    p k ⁡ ( ≤ m , n ) restricted-partitions-P-at-most 𝑘 absent 𝑚 𝑛 {\displaystyle{\displaystyle p_{\NVar{k}}\left(\leq\NVar{m},\NVar{n}\right)}}
    xml-id
    C26.S9.SS1.m1adec
    0 references
    Q12174
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C26.S1.XMD4.m1cdec
    0 references
    Q12171
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C26.S1.XMD5.m1bdec
    0 references
    Q12172
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C26.S1.XMD6.m1fdec
    0 references
    Q12189
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C26.S9.XMD1.m1bdec
    0 references
     
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