DLMF:5.11.E18 (Q2144): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older edit
‎Changed an Item: Wikidata Toolkit example test statement addition
‎Changed an Item: Add constraint
 
(4 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q10754 / rank
 
Normal rank
Property / Symbols used: Q10754 / qualifier
 
Defining formula:

( 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.m1acdec
Property / Symbols used
 
Property / Symbols used: Q11289 / rank
 
Normal rank
Property / Symbols used: Q11289 / qualifier
 
Defining formula:

B n ( ℓ ) ⁡ ( x ) generalized-Bernoulli-polynomial-B ℓ 𝑛 𝑥 {\displaystyle{\displaystyle B^{(\NVar{\ell})}_{\NVar{n}}\left(\NVar{x}\right)}}

\genBernoullipolyB{\NVar{\ell}}{\NVar{n}}@{\NVar{x}}
Property / Symbols used: Q11289 / qualifier
 
xml-id: C24.S16.Px1.p1.m3aadec
Property / Symbols used
 
Property / Symbols used: Q11279 / rank
 
Normal rank
Property / Symbols used: Q11279 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11279 / qualifier
 
xml-id: C5.S1.XMD4.m1jdec
Property / Symbols used
 
Property / Symbols used: Q11275 / rank
 
Normal rank
Property / Symbols used: Q11275 / qualifier
 
Defining formula:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q11275 / qualifier
 
xml-id: C5.S1.XMD8.m1fdec
Property / Symbols used
 
Property / Symbols used: Q11283 / rank
 
Normal rank
Property / Symbols used: Q11283 / qualifier
 
Defining formula:

b 𝑏 {\displaystyle{\displaystyle b}}

b
Property / Symbols used: Q11283 / qualifier
 
xml-id: C5.S1.XMD9.m1gdec

Latest revision as of 19:42, 1 January 2020

No description defined
Language Label Description Also known as
English
DLMF:5.11.E18
No description defined

    Statements

    Defining formula
    H k ⁢ ( a , b ) = ( a - b 2 ⁢ k ) ⁢ B 2 ⁢ k ( a - b + 1 ) ⁡ ( a - b + 1 2 ) . subscript 𝐻 𝑘 𝑎 𝑏 binomial 𝑎 𝑏 2 𝑘 generalized-Bernoulli-polynomial-B 𝑎 𝑏 1 2 𝑘 𝑎 𝑏 1 2 {\displaystyle{\displaystyle H_{k}(a,b)=\genfrac{(}{)}{0.0pt}{}{a-b}{2k}B^{(a-% b+1)}_{2k}\left(\frac{a-b+1}{2}\right).}}
    0 references
    DLMF id
    DLMF:5.11.E18
    0 references
    Symbols used
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1acdec
    0 references
    Q11289
    Defining formula
    B n ( ℓ ) ⁡ ( x ) generalized-Bernoulli-polynomial-B ℓ 𝑛 𝑥 {\displaystyle{\displaystyle B^{(\NVar{\ell})}_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C24.S16.Px1.p1.m3aadec
    0 references
    Q11279
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C5.S1.XMD4.m1jdec
    0 references
    Q11275
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C5.S1.XMD8.m1fdec
    0 references
    Q11283
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C5.S1.XMD9.m1gdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q2144&oldid=28917"