DLMF:2.11.E32 (Q1062)

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DLMF:2.11.E32
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    Statements

    Defining formula
    d n = ∑ j = 0 n ( - 1 ) j ⁢ ( n j ) ⁢ ( j + 1 ) n - 1 ⁢ s j a j + 1 ∑ j = 0 n ( - 1 ) j ⁢ ( n j ) ⁢ ( j + 1 ) n - 1 ⁢ 1 a j + 1 . subscript 𝑑 𝑛 superscript subscript 𝑗 0 𝑛 superscript 1 𝑗 binomial 𝑛 𝑗 superscript 𝑗 1 𝑛 1 subscript 𝑠 𝑗 subscript 𝑎 𝑗 1 superscript subscript 𝑗 0 𝑛 superscript 1 𝑗 binomial 𝑛 𝑗 superscript 𝑗 1 𝑛 1 1 subscript 𝑎 𝑗 1 {\displaystyle{\displaystyle d_{n}=\frac{\sum_{j=0}^{n}(-1)^{j}\genfrac{(}{)}{% 0.0pt}{}{n}{j}(j+1)^{n-1}\frac{s_{j}}{a_{j+1}}}{\sum_{j=0}^{n}(-1)^{j}\genfrac% {(}{)}{0.0pt}{}{n}{j}(j+1)^{n-1}\frac{1}{a_{j+1}}}.}}
    0 references
    DLMF id
    DLMF:2.11.E32
    0 references
    Symbols used
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1adec
    0 references
    Q11145
    Defining formula
    a n subscript 𝑎 𝑛 {\displaystyle{\displaystyle a_{n}}}
    xml-id
    C2.S11.XMD12.m1cdec
    0 references
     
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