DLMF:2.10.E7 (Q994): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10931 / rank
 
Normal rank
Property / Symbols used: Q10931 / qualifier
 
test:

∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}

\asympexp
Property / Symbols used: Q10931 / qualifier
 
xml-id: C2.S1.SS3.p1.m11adec
Property / Symbols used
 
Property / Symbols used: Q10754 / rank
 
Normal rank
Property / Symbols used: Q10754 / qualifier
 
test:

( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}

\binom{\NVar{m}}{\NVar{n}}
Property / Symbols used: Q10754 / qualifier
 
xml-id: C1.S2.SS1.m1adec
Property / Symbols used
 
Property / Symbols used: Q11113 / rank
 
Normal rank
Property / Symbols used: Q11113 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11113 / qualifier
 
xml-id: C2.S10.XMD3.m1edec

Latest revision as of 16:34, 1 January 2020

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DLMF:2.10.E7
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    Statements

    test
    ∑ 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
    Symbols used
    Q11109
    test
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1addec
    0 references
    Riemann zeta function
    test
    ζ ⁡ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    xml-id
    C25.S2.E1.m2aadec
    0 references
    Q10931
    test
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11adec
    0 references
    Q10754
    test
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1adec
    0 references
    Q11113
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C2.S10.XMD3.m1edec
    0 references
     
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