DLMF:2.10.E7 (Q994)

From DRMF
Revision as of 16:55, 30 December 2019 by Admin (talk | contribs) (‎Changed an Item: Add constraint)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:2.10.E7
No description defined

    Statements

    Defining formula
    ∑ j = 1 n - 1 j α ∼ ζ ⁡ ( - α ) + n α + 1 α + 1 ⁢ ∑ s = 0 ∞ ( α + 1 s ) ⁢ B s n s , asymptotic-expansion superscript subscript 𝑗 1 𝑛 1 superscript 𝑗 𝛼 Riemann-zeta 𝛼 superscript 𝑛 𝛼 1 𝛼 1 superscript subscript 𝑠 0 binomial 𝛼 1 𝑠 Bernoulli-number-B 𝑠 superscript 𝑛 𝑠 {\displaystyle{\displaystyle\sum_{j=1}^{n-1}j^{\alpha}\sim\zeta\left(-\alpha% \right)+\frac{n^{\alpha+1}}{\alpha+1}\sum_{s=0}^{\infty}\genfrac{(}{)}{0.0pt}{% }{\alpha+1}{s}\frac{B_{s}}{n^{s}},}}
    0 references
    DLMF id
    DLMF:2.10.E7
    0 references
    constraint
    n → ∞ → 𝑛 {\displaystyle{\displaystyle n\to\infty}}
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q994&oldid=17683"