DLMF:26.12.E26 (Q7943): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12211 / rank
 
Normal rank
Property / Symbols used: Q12211 / qualifier
 
Defining formula:

pp ⁡ ( n ) plane-partitions-PP 𝑛 {\displaystyle{\displaystyle\mathrm{pp}\left(\NVar{n}\right)}}

\nplanepartitions@{\NVar{n}}
Property / Symbols used: Q12211 / qualifier
 
xml-id: C26.S12.SS1.p4.m4abdec
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.m1bdec
Property / Symbols used
 
Property / Symbols used: Q12210 / rank
 
Normal rank
Property / Symbols used: Q12210 / qualifier
 
Defining formula:

π 𝜋 {\displaystyle{\displaystyle\pi}}

\pi
Property / Symbols used: Q12210 / qualifier
 
xml-id: C26.S12.XMD1.m1edec

Latest revision as of 14:06, 2 January 2020

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DLMF:26.12.E26
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    Statements

    Defining formula
    pp ⁡ ( n ) ∼ ( ζ ⁡ ( 3 ) ) 7 / 36 2 11 / 36 ⁢ ( 3 ⁢ π ) 1 / 2 ⁢ n 25 / 36 ⁢ exp ⁡ ( 3 ⁢ ( ζ ⁡ ( 3 ) ) 1 / 3 ⁢ ( 1 2 ⁢ n ) 2 / 3 + ζ ′ ⁡ ( - 1 ) ) , asymptotically-equals plane-partitions-PP 𝑛 superscript Riemann-zeta 3 7 36 superscript 2 11 36 superscript 3 𝜋 1 2 superscript 𝑛 25 36 3 superscript Riemann-zeta 3 1 3 superscript 1 2 𝑛 2 3 diffop Riemann-zeta 1 1 {\displaystyle{\displaystyle\mathrm{pp}\left(n\right)\sim\frac{\left(\zeta% \left(3\right)\right)^{7/36}}{2^{11/36}(3\pi)^{1/2}n^{25/36}}\exp\left(3\left(% \zeta\left(3\right)\right)^{1/3}\left(\tfrac{1}{2}n\right)^{2/3}+\zeta'\left(-% 1\right)\right),}}
    0 references
    DLMF id
    DLMF:26.12.E26
    0 references
    Symbols used
    Riemann zeta function
    Defining formula
    ζ ⁡ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    xml-id
    C25.S2.E1.m2adec
    0 references
    asymptotic equality
    Defining formula
    ∼ asymptotically-equals {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.E1.m2adec
    0 references
    exponential function
    Defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2adec
    0 references
    Q12211
    Defining formula
    pp ⁡ ( n ) plane-partitions-PP 𝑛 {\displaystyle{\displaystyle\mathrm{pp}\left(\NVar{n}\right)}}
    xml-id
    C26.S12.SS1.p4.m4abdec
    0 references
    Q12172
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C26.S1.XMD6.m1bdec
    0 references
    Q12210
    Defining formula
    π 𝜋 {\displaystyle{\displaystyle\pi}}
    xml-id
    C26.S12.XMD1.m1edec
    0 references
     
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