DLMF:26.10.E11 (Q7894): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10784 / rank
 
Normal rank
Property / Symbols used: Q10784 / qualifier
 
Defining formula:

∈ {\displaystyle{\displaystyle\in}}

\in
Property / Symbols used: Q10784 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r10.m2acdec
Property / Symbols used
 
Property / Symbols used: Q12191 / rank
 
Normal rank
Property / Symbols used: Q12191 / qualifier
 
Defining formula:

p ⁡ ( condition , n ) restricted-partitions-P condition 𝑛 {\displaystyle{\displaystyle p\left(\NVar{\mathrm{condition}},\NVar{n}\right)}}

\nrestpartitions[]@{\NVar{\mathrm{condition}}}{\NVar{n}}
Property / Symbols used: Q12191 / qualifier
 
xml-id: C26.S10.SS1.m4aidec
Property / Symbols used
 
Property / Symbols used: Q12176 / rank
 
Normal rank
Property / Symbols used: Q12176 / qualifier
 
Defining formula:

j 𝑗 {\displaystyle{\displaystyle j}}

j
Property / Symbols used: Q12176 / qualifier
 
xml-id: C26.S1.XMD3.m1edec
Property / Symbols used
 
Property / Symbols used: Q12172 / rank
 
Normal rank
Property / Symbols used: Q12172 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12172 / qualifier
 
xml-id: C26.S1.XMD6.m1jdec
Property / Symbols used
 
Property / Symbols used: Q12192 / rank
 
Normal rank
Property / Symbols used: Q12192 / qualifier
 
Defining formula:

S 𝑆 {\displaystyle{\displaystyle S}}

S
Property / Symbols used: Q12192 / qualifier
 
xml-id: C26.S10.XMD1.m1bdec

Latest revision as of 14:00, 2 January 2020

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DLMF:26.10.E11
No description defined

    Statements

    Defining formula
    p ⁡ ( ∈ S , n ) = 1 n ⁢ ∑ t = 1 n p ⁡ ( ∈ S , n - t ) ⁢ ∑ j | t j ∈ S j , restricted-partitions-P absent 𝑆 𝑛 1 𝑛 superscript subscript 𝑡 1 𝑛 restricted-partitions-P absent 𝑆 𝑛 𝑡 subscript divides 𝑗 𝑡 𝑗 𝑆 𝑗 {\displaystyle{\displaystyle p\left(\in\!S,n\right)=\frac{1}{n}\sum_{t=1}^{n}p% \left(\in\!S,n-t\right)\sum_{\begin{subarray}{c}j\mathbin{|}t\\ j\in S\end{subarray}}j,}}
    0 references
    DLMF id
    DLMF:26.10.E11
    0 references
    Symbols used
    Q10784
    Defining formula
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2acdec
    0 references
    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.m4aidec
    0 references
    Q12176
    Defining formula
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C26.S1.XMD3.m1edec
    0 references
    Q12172
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C26.S1.XMD6.m1jdec
    0 references
    Q12192
    Defining formula
    S 𝑆 {\displaystyle{\displaystyle S}}
    xml-id
    C26.S10.XMD1.m1bdec
    0 references
     
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