DLMF:24.14.E1 (Q7546)

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DLMF:24.14.E1
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    Statements

    test
    ∑ k = 0 n ( n k ) ⁢ B k ⁡ ( x ) ⁢ B n - k ⁡ ( y ) = n ⁢ ( x + y - 1 ) ⁢ B n - 1 ⁡ ( x + y ) - ( n - 1 ) ⁢ B n ⁡ ( x + y ) , superscript subscript 𝑘 0 𝑛 binomial 𝑛 𝑘 Bernoulli-polynomial-B 𝑘 𝑥 Bernoulli-polynomial-B 𝑛 𝑘 𝑦 𝑛 𝑥 𝑦 1 Bernoulli-polynomial-B 𝑛 1 𝑥 𝑦 𝑛 1 Bernoulli-polynomial-B 𝑛 𝑥 𝑦 {\displaystyle{\displaystyle\sum_{k=0}^{n}{n\choose k}B_{k}\left(x\right)B_{n-% k}\left(y\right)=n(x+y-1)B_{n-1}\left(x+y\right)-(n-1)B_{n}\left(x+y\right),}}
    0 references
    DLMF id
    DLMF:24.14.E1
    0 references
    Symbols used
    Q11288
    test
    B n ⁡ ( x ) Bernoulli-polynomial-B 𝑛 𝑥 {\displaystyle{\displaystyle B_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C24.S2.SS1.m2adec
    0 references
     
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