DLMF:3.9.E13 (Q1400)

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DLMF:3.9.E13
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    Statements

    Defining formula
    ℒ k ( n ) ⁢ ( s ) = ∑ j = 0 k ( - 1 ) j ⁢ ( k j ) ⁢ c j , k , n ⁢ s n + j / a n + j + 1 ∑ j = 0 k ( - 1 ) j ⁢ ( k j ) ⁢ c j , k , n / a n + j + 1 , superscript subscript ℒ 𝑘 𝑛 𝑠 superscript subscript 𝑗 0 𝑘 superscript 1 𝑗 binomial 𝑘 𝑗 subscript 𝑐 𝑗 𝑘 𝑛 subscript 𝑠 𝑛 𝑗 subscript 𝑎 𝑛 𝑗 1 superscript subscript 𝑗 0 𝑘 superscript 1 𝑗 binomial 𝑘 𝑗 subscript 𝑐 𝑗 𝑘 𝑛 subscript 𝑎 𝑛 𝑗 1 {\displaystyle{\displaystyle{\cal L}_{k}^{(n)}(s)=\frac{\sum_{j=0}^{k}(-1)^{j}% \genfrac{(}{)}{0.0pt}{}{k}{j}c_{j,k,n}\ifrac{s_{n+j}}{a_{n+j+1}}}{\sum_{j=0}^{% k}(-1)^{j}\genfrac{(}{)}{0.0pt}{}{k}{j}c_{j,k,n}/a_{n+j+1}},}}
    0 references
    DLMF id
    DLMF:3.9.E13
    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.m1aadec
    0 references
    Q11201
    Defining formula
    s n subscript 𝑠 𝑛 {\displaystyle{\displaystyle s_{n}}}
    xml-id
    C3.S9.XMD6.m1dec
    0 references
    coefficient (locally)
    Defining formula
    c j , k , n subscript 𝑐 𝑗 𝑘 𝑛 {\displaystyle{\displaystyle c_{j,k,n}}}
    xml-id
    C3.S9.XMD7.m1dec
    0 references
     
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