DLMF:13.8.E16 (Q4442)

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DLMF:13.8.E16
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    Statements

    Defining formula
    ( k + 1 ) ⁢ c k + 1 ⁢ ( z ) + ∑ s = 0 k ( b ⁢ B s + 1 ( s + 1 ) ! + z ⁢ ( s + 1 ) ⁢ B s + 2 ( s + 2 ) ! ) ⁢ c k - s ⁢ ( z ) = 0 , 𝑘 1 subscript 𝑐 𝑘 1 𝑧 superscript subscript 𝑠 0 𝑘 𝑏 Bernoulli-number-B 𝑠 1 𝑠 1 𝑧 𝑠 1 Bernoulli-number-B 𝑠 2 𝑠 2 subscript 𝑐 𝑘 𝑠 𝑧 0 {\displaystyle{\displaystyle(k+1)c_{k+1}(z)+\sum_{s=0}^{k}\left(\frac{bB_{s+1}% }{(s+1)!}+\frac{z(s+1)B_{s+2}}{(s+2)!}\right)c_{k-s}(z)=0,}}
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    DLMF id
    DLMF:13.8.E16
    0 references
    constraint
    k = 0 , 1 , 2 , … 𝑘 0 1 2 … {\displaystyle{\displaystyle k=0,1,2,\dots}}
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    Symbols used
    Q11109
    Defining formula
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1adec
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