DLMF:2.10.E12 (Q999)

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DLMF:2.10.E12
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    Statements

    Defining formula
    | S ⁢ ( α , β , n ) | ≤ ∑ j = 1 n - 1 j α = O ⁡ ( 1 ) , O ⁡ ( ln ⁡ n ) ,  or  ⁢ O ⁡ ( n α + 1 ) , formulae-sequence 𝑆 𝛼 𝛽 𝑛 superscript subscript 𝑗 1 𝑛 1 superscript 𝑗 𝛼 Big-O 1 Big-O 𝑛  or  Big-O superscript 𝑛 𝛼 1 {\displaystyle{\displaystyle|S(\alpha,\beta,n)|\leq\sum_{j=1}^{n-1}j^{\alpha}=% O\left(1\right),\;O\left(\ln n\right),\text{ or }O\left(n^{\alpha+1}\right),}}
    0 references
    DLMF id
    DLMF:2.10.E12
    0 references
    Symbols used
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2adec
    0 references
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2addec
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    Q11121
    Defining formula
    S ⁢ ( α , β , n ) 𝑆 𝛼 𝛽 𝑛 {\displaystyle{\displaystyle S(\alpha,\beta,n)}}
    xml-id
    C2.S10.XMD11.m1adec
    0 references
     
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