DLMF:24.15.E6 (Q7563): Difference between revisions

From DRMF
Jump to navigation Jump to search
Changed an Item: Add constraint
Changed an Item: Add constraint
 
(3 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q12131 / rank
 
Normal rank
Property / Symbols used: Q12131 / qualifier
 
Defining formula:

S ( n , k ) Stirling-number-second-kind-S 𝑛 𝑘 {\displaystyle{\displaystyle S\left(\NVar{n},\NVar{k}\right)}}

\StirlingnumberS@{\NVar{n}}{\NVar{k}}
Property / Symbols used: Q12131 / qualifier
 
xml-id: C26.S8.SS1.p3.m2adec
Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
Defining formula:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5abdec
Property / Symbols used
 
Property / Symbols used: Q12113 / rank
 
Normal rank
Property / Symbols used: Q12113 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q12113 / qualifier
 
xml-id: C24.S1.XMD2.m1dec
Property / Symbols used
 
Property / Symbols used: Q12110 / rank
 
Normal rank
Property / Symbols used: Q12110 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12110 / qualifier
 
xml-id: C24.S1.XMD5.m1fdec

Latest revision as of 01:48, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:24.15.E6
No description defined

    Statements

    B n = k = 0 n ( - 1 ) k k ! S ( n , k ) k + 1 , Bernoulli-number-B 𝑛 superscript subscript 𝑘 0 𝑛 superscript 1 𝑘 𝑘 Stirling-number-second-kind-S 𝑛 𝑘 𝑘 1 {\displaystyle{\displaystyle B_{n}=\sum_{k=0}^{n}(-1)^{k}\frac{k!S\left(n,k% \right)}{k+1},}}
    0 references
    DLMF:24.15.E6
    0 references
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    C24.S2.SS1.m1abdec
    0 references
    S ( n , k ) Stirling-number-second-kind-S 𝑛 𝑘 {\displaystyle{\displaystyle S\left(\NVar{n},\NVar{k}\right)}}
    C26.S8.SS1.p3.m2adec
    0 references
    ! {\displaystyle{\displaystyle!}}
    introduction.Sx4.p1.t1.r15.m5abdec
    0 references
    k 𝑘 {\displaystyle{\displaystyle k}}
    C24.S1.XMD2.m1dec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C24.S1.XMD5.m1fdec
    0 references