DLMF:24.14.E1 (Q7546): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older edit
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
(One intermediate revision by the same user not shown)
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.m1dec
Property / Symbols used
 
Property / Symbols used: Q12112 / rank
 
Normal rank
Property / Symbols used: Q12112 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q12112 / qualifier
 
xml-id: C24.S1.XMD7.m1dec

Latest revision as of 01:45, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:24.14.E1
No description defined

    Statements

    Defining formula
    ∑ k = 0 n ( n k ) ⁢ B k ⁡ ( x ) ⁢ B n - k ⁡ ( y ) = n ⁢ ( x + y - 1 ) ⁢ B n - 1 ⁡ ( x + y ) - ( n - 1 ) ⁢ B n ⁡ ( x + y ) , superscript subscript 𝑘 0 𝑛 binomial 𝑛 𝑘 Bernoulli-polynomial-B 𝑘 𝑥 Bernoulli-polynomial-B 𝑛 𝑘 𝑦 𝑛 𝑥 𝑦 1 Bernoulli-polynomial-B 𝑛 1 𝑥 𝑦 𝑛 1 Bernoulli-polynomial-B 𝑛 𝑥 𝑦 {\displaystyle{\displaystyle\sum_{k=0}^{n}{n\choose k}B_{k}\left(x\right)B_{n-% k}\left(y\right)=n(x+y-1)B_{n-1}\left(x+y\right)-(n-1)B_{n}\left(x+y\right),}}
    0 references
    DLMF id
    DLMF:24.14.E1
    0 references
    Symbols used
    Q11288
    Defining formula
    B n ⁡ ( x ) Bernoulli-polynomial-B 𝑛 𝑥 {\displaystyle{\displaystyle B_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C24.S2.SS1.m2adec
    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.m1dec
    0 references
    Q12110
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1dec
    0 references
    Q12112
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C24.S1.XMD7.m1dec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q7546&oldid=34343"