DLMF:5.11.E17 (Q2143): Difference between revisions

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Created a new Item: Wikidata Toolkit example test item creation
 
Changed an Item: Add constraint
 
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Property / Symbols defined
 
Property / Symbols defined: coefficients (locally) / rank
 
Normal rank
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.m1abdec
Property / Symbols used
 
Property / Symbols used: Q11289 / rank
 
Normal rank
Property / Symbols used: Q11289 / qualifier
 
Defining formula:

B n ( ) ( x ) generalized-Bernoulli-polynomial-B 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.m3adec
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.m1idec
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.m1edec
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.m1fdec

Latest revision as of 19:42, 1 January 2020

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DLMF:5.11.E17
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    Statements

    G k ( a , b ) = ( a - b k ) B k ( a - b + 1 ) ( a ) , subscript 𝐺 𝑘 𝑎 𝑏 binomial 𝑎 𝑏 𝑘 generalized-Bernoulli-polynomial-B 𝑎 𝑏 1 𝑘 𝑎 {\displaystyle{\displaystyle G_{k}(a,b)=\genfrac{(}{)}{0.0pt}{}{a-b}{k}B^{(a-b% +1)}_{k}\left(a\right),}}
    0 references
    DLMF:5.11.E17
    0 references
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    C1.S2.SS1.m1abdec
    0 references
    B n ( ) ( x ) generalized-Bernoulli-polynomial-B 𝑛 𝑥 {\displaystyle{\displaystyle B^{(\NVar{\ell})}_{\NVar{n}}\left(\NVar{x}\right)}}
    C24.S16.Px1.p1.m3adec
    0 references
    k 𝑘 {\displaystyle{\displaystyle k}}
    C5.S1.XMD4.m1idec
    0 references
    a 𝑎 {\displaystyle{\displaystyle a}}
    C5.S1.XMD8.m1edec
    0 references
    b 𝑏 {\displaystyle{\displaystyle b}}
    C5.S1.XMD9.m1fdec
    0 references