DLMF:24.4.E29 (Q7442): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11288 / rank
 
Normal rank
Property / Symbols used: Q11288 / qualifier
 
Defining formula:

B n ⁡ ( x ) Bernoulli-polynomial-B 𝑛 𝑥 {\displaystyle{\displaystyle B_{\NVar{n}}\left(\NVar{x}\right)}}

\BernoullipolyB{\NVar{n}}@{\NVar{x}}
Property / Symbols used: Q11288 / qualifier
 
xml-id: C24.S2.SS1.m2andec
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.m1abdec

Latest revision as of 01:28, 2 January 2020

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DLMF:24.4.E29
No description defined

    Statements

    Defining formula
    B 2 ⁢ n ⁡ ( 1 3 ) = B 2 ⁢ n ⁡ ( 2 3 ) = - 1 2 ⁢ ( 1 - 3 1 - 2 ⁢ n ) ⁢ B 2 ⁢ n . Bernoulli-polynomial-B 2 𝑛 1 3 Bernoulli-polynomial-B 2 𝑛 2 3 1 2 1 superscript 3 1 2 𝑛 Bernoulli-number-B 2 𝑛 {\displaystyle{\displaystyle B_{2n}\left(\tfrac{1}{3}\right)=B_{2n}\left(% \tfrac{2}{3}\right)=-\tfrac{1}{2}(1-3^{1-2n})B_{2n}.}}
    0 references
    DLMF id
    DLMF:24.4.E29
    0 references
    Symbols used
    Q11109
    Defining formula
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1aidec
    0 references
    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.m2andec
    0 references
    Q12110
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1abdec
    0 references
     
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