DLMF:27.14.E9 (Q8108): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / rank
 
Normal rank
Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / qualifier
 
Defining formula:

d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}

\deriv{\NVar{f}}{\NVar{x}}
Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / qualifier
 
xml-id: C1.S4.E4.m2adec
Property / Symbols used
 
Property / Symbols used: hyperbolic sine function / rank
 
Normal rank
Property / Symbols used: hyperbolic sine function / qualifier
 
Defining formula:

sinh ⁡ z 𝑧 {\displaystyle{\displaystyle\sinh\NVar{z}}}

\sinh@@{\NVar{z}}
Property / Symbols used: hyperbolic sine function / qualifier
 
xml-id: C4.S28.E1.m2adec
Property / Symbols used
 
Property / Symbols used: Q12187 / rank
 
Normal rank
Property / Symbols used: Q12187 / qualifier
 
Defining formula:

p ⁡ ( n ) partition-function 𝑛 {\displaystyle{\displaystyle p\left(\NVar{n}\right)}}

\npartitions[]@{\NVar{n}}
Property / Symbols used: Q12187 / qualifier
 
xml-id: C26.S2.Px4.p2.m5addec
Property / Symbols used
 
Property / Symbols used: Q12238 / rank
 
Normal rank
Property / Symbols used: Q12238 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q12238 / qualifier
 
xml-id: C27.S1.XMD2.m1ddec
Property / Symbols used
 
Property / Symbols used: Q12234 / rank
 
Normal rank
Property / Symbols used: Q12234 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12234 / qualifier
 
xml-id: C27.S1.XMD4.m1edec
Property / Symbols used
 
Property / Symbols used: Q12266 / rank
 
Normal rank
Property / Symbols used: Q12266 / qualifier
 
Defining formula:

A k ⁢ ( n ) subscript 𝐴 𝑘 𝑛 {\displaystyle{\displaystyle A_{k}(n)}}

A_{k}(n)
Property / Symbols used: Q12266 / qualifier
 
xml-id: C27.S14.XMD2.m1dec

Latest revision as of 14:30, 2 January 2020

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DLMF:27.14.E9
No description defined

    Statements

    Defining formula
    p ⁡ ( n ) = 1 π ⁢ 2 ⁢ ∑ k = 1 ∞ k ⁢ A k ⁢ ( n ) ⁢ [ d d t ⁡ sinh ⁡ ( K ⁢ t / k ) t ] t = n - ( 1 / 24 ) , partition-function 𝑛 1 2 superscript subscript 𝑘 1 𝑘 subscript 𝐴 𝑘 𝑛 subscript delimited-[] derivative 𝑡 𝐾 𝑡 𝑘 𝑡 𝑡 𝑛 1 24 {\displaystyle{\displaystyle p\left(n\right)=\frac{1}{\pi\sqrt{2}}\sum_{k=1}^{% \infty}\sqrt{k}A_{k}(n)\*\left[\frac{\mathrm{d}}{\mathrm{d}t}\frac{\sinh\left(% \ifrac{K\sqrt{t}}{k}\right)}{\sqrt{t}}\right]_{t=n-(1/24)},}}
    0 references
    DLMF id
    DLMF:27.14.E9
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
    0 references
    derivative of $$f$$ with respect to $$x$$
    Defining formula
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2adec
    0 references
    hyperbolic sine function
    Defining formula
    sinh ⁡ z 𝑧 {\displaystyle{\displaystyle\sinh\NVar{z}}}
    xml-id
    C4.S28.E1.m2adec
    0 references
    Q12187
    Defining formula
    p ⁡ ( n ) partition-function 𝑛 {\displaystyle{\displaystyle p\left(\NVar{n}\right)}}
    xml-id
    C26.S2.Px4.p2.m5addec
    0 references
    Q12238
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C27.S1.XMD2.m1ddec
    0 references
    Q12234
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C27.S1.XMD4.m1edec
    0 references
    Q12266
    Defining formula
    A k ⁢ ( n ) subscript 𝐴 𝑘 𝑛 {\displaystyle{\displaystyle A_{k}(n)}}
    xml-id
    C27.S14.XMD2.m1dec
    0 references
     
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