DLMF:24.15.E7 (Q7564): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older edit
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
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.m1gdec

Latest revision as of 01:48, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:24.15.E7
No description defined

    Statements

    Defining formula
    B n = ∑ k = 0 n ( - 1 ) k ⁢ ( n + 1 k + 1 ) ⁢ S ⁡ ( n + k , k ) / ( n + k k ) , Bernoulli-number-B 𝑛 superscript subscript 𝑘 0 𝑛 superscript 1 𝑘 binomial 𝑛 1 𝑘 1 Stirling-number-second-kind-S 𝑛 𝑘 𝑘 binomial 𝑛 𝑘 𝑘 {\displaystyle{\displaystyle B_{n}=\sum_{k=0}^{n}(-1)^{k}\genfrac{(}{)}{0.0pt}% {}{n+1}{k+1}S\left(n+k,k\right)\bigg{/}\genfrac{(}{)}{0.0pt}{}{n+k}{k},}}
    0 references
    DLMF id
    DLMF:24.15.E7
    0 references
    Symbols used
    Q11109
    Defining formula
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1acdec
    0 references
    Q12131
    Defining formula
    S ⁡ ( n , k ) Stirling-number-second-kind-S 𝑛 𝑘 {\displaystyle{\displaystyle S\left(\NVar{n},\NVar{k}\right)}}
    xml-id
    C26.S8.SS1.p3.m2aadec
    0 references
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1adec
    0 references
    Q12113
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C24.S1.XMD2.m1adec
    0 references
    Q12110
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1gdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q7564&oldid=34808"