DLMF:26.14.E5 (Q7956): Difference between revisions

From testwiki
Jump to navigation Jump to search
imported>Admin
 
imported>Admin
 
(4 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q12217 / rank
 
Normal rank
Property / Symbols used: Q12217 / qualifier
 
test:

n k Eulerian-number 𝑛 𝑘 {\displaystyle{\displaystyle\genfrac{<}{>}{0.0pt}{}{\NVar{n}}{\NVar{k}}}}

\Euleriannumber{\NVar{n}}{\NVar{k}}
Property / Symbols used: Q12217 / qualifier
 
xml-id: C26.S14.SS1.p3.m2abdec
Property / Symbols used
 
Property / Symbols used: Q10754 / rank
 
Normal rank
Property / Symbols used: Q10754 / qualifier
 
test:

( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}

\binom{\NVar{m}}{\NVar{n}}
Property / Symbols used: Q10754 / qualifier
 
xml-id: C1.S2.SS1.m1adec
Property / Symbols used
 
Property / Symbols used: Q12173 / rank
 
Normal rank
Property / Symbols used: Q12173 / qualifier
 
test:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q12173 / qualifier
 
xml-id: C26.S1.XMD1.m1adec
Property / Symbols used
 
Property / Symbols used: Q12174 / rank
 
Normal rank
Property / Symbols used: Q12174 / qualifier
 
test:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q12174 / qualifier
 
xml-id: C26.S1.XMD4.m1cdec
Property / Symbols used
 
Property / Symbols used: Q12172 / rank
 
Normal rank
Property / Symbols used: Q12172 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12172 / qualifier
 
xml-id: C26.S1.XMD6.m1edec

Latest revision as of 13:08, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:26.14.E5
No description defined

    Statements

    k = 0 n - 1 n k ( x + k n ) = x n . superscript subscript 𝑘 0 𝑛 1 Eulerian-number 𝑛 𝑘 binomial 𝑥 𝑘 𝑛 superscript 𝑥 𝑛 {\displaystyle{\displaystyle\sum_{k=0}^{n-1}\genfrac{<}{>}{0.0pt}{}{n}{k}% \genfrac{(}{)}{0.0pt}{}{x+k}{n}=x^{n}.}}
    0 references
    0 references
    n k Eulerian-number 𝑛 𝑘 {\displaystyle{\displaystyle\genfrac{<}{>}{0.0pt}{}{\NVar{n}}{\NVar{k}}}}
    C26.S14.SS1.p3.m2abdec
    0 references
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    C1.S2.SS1.m1adec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C26.S1.XMD1.m1adec
    0 references
    k 𝑘 {\displaystyle{\displaystyle k}}
    C26.S1.XMD4.m1cdec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C26.S1.XMD6.m1edec
    0 references