DLMF:26.15.E10 (Q7977): 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: Q12174 / rank
 
Normal rank
Property / Symbols used: Q12174 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q12174 / qualifier
 
xml-id: C26.S1.XMD4.m1fdec
Property / Symbols used
 
Property / Symbols used: Q12172 / rank
 
Normal rank
Property / Symbols used: Q12172 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12172 / qualifier
 
xml-id: C26.S1.XMD6.m1edec
Property / Symbols used
 
Property / Symbols used: Q12220 / rank
 
Normal rank
Property / Symbols used: Q12220 / qualifier
 
Defining formula:

B 𝐵 {\displaystyle{\displaystyle B}}

B
Property / Symbols used: Q12220 / qualifier
 
xml-id: C26.S15.XMD2.m1gdec
Property / Symbols used
 
Property / Symbols used: Q12223 / rank
 
Normal rank
Property / Symbols used: Q12223 / qualifier
 
Defining formula:

N ( x , B ) 𝑁 𝑥 𝐵 {\displaystyle{\displaystyle N(x,B)}}

N(x,B)
Property / Symbols used: Q12223 / qualifier
 
xml-id: C26.S15.XMD6.m1cdec

Latest revision as of 14:11, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:26.15.E10
No description defined

    Statements

    2 ( n ! ) N 0 ( B ) = 2 ( n ! ) k = 0 n ( - 1 ) k 2 n 2 n - k ( 2 n - k k ) ( n - k ) ! . 2 𝑛 subscript 𝑁 0 𝐵 2 𝑛 superscript subscript 𝑘 0 𝑛 superscript 1 𝑘 2 𝑛 2 𝑛 𝑘 binomial 2 𝑛 𝑘 𝑘 𝑛 𝑘 {\displaystyle{\displaystyle 2(n!)N_{0}(B)=2(n!)\sum_{k=0}^{n}(-1)^{k}\frac{2n% }{2n-k}\genfrac{(}{)}{0.0pt}{}{2n-k}{k}{(n-k)!}.}}
    0 references
    DLMF:26.15.E10
    0 references
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    C1.S2.SS1.m1aadec
    0 references
    ! {\displaystyle{\displaystyle!}}
    introduction.Sx4.p1.t1.r15.m5abdec
    0 references
    k 𝑘 {\displaystyle{\displaystyle k}}
    C26.S1.XMD4.m1fdec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C26.S1.XMD6.m1edec
    0 references
    B 𝐵 {\displaystyle{\displaystyle B}}
    C26.S15.XMD2.m1gdec
    0 references
    N ( x , B ) 𝑁 𝑥 𝐵 {\displaystyle{\displaystyle N(x,B)}}
    C26.S15.XMD6.m1cdec
    0 references