DLMF:24.13.E6 (Q7540): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
test:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1aedec

Revision as of 00:44, 2 January 2020

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DLMF:24.13.E6
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    Statements

    test
    ∫ 0 1 B n ⁡ ( t ) ⁢ B m ⁡ ( t ) ⁢ d t = ( - 1 ) n - 1 ⁢ m ! ⁢ n ! ( m + n ) ! ⁢ B m + n . superscript subscript 0 1 Bernoulli-polynomial-B 𝑛 𝑡 Bernoulli-polynomial-B 𝑚 𝑡 𝑡 superscript 1 𝑛 1 𝑚 𝑛 𝑚 𝑛 Bernoulli-number-B 𝑚 𝑛 {\displaystyle{\displaystyle\int_{0}^{1}B_{n}\left(t\right)B_{m}\left(t\right)% \mathrm{d}t=\frac{(-1)^{n-1}m!n!}{(m+n)!}B_{m+n}.}}
    0 references
    DLMF id
    DLMF:24.13.E6
    0 references
    Symbols used
    Q11109
    test
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1aadec
    0 references
    Q11288
    test
    B n ⁡ ( x ) Bernoulli-polynomial-B 𝑛 𝑥 {\displaystyle{\displaystyle B_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C24.S2.SS1.m2aedec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aedec
    0 references
     
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