DLMF:24.16.E8 (Q7578): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11109 / rank
 
Normal rank
Property / Symbols used: Q11109 / qualifier
 
test:

B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}

\BernoullinumberB{\NVar{n}}
Property / Symbols used: Q11109 / qualifier
 
xml-id: C24.S2.SS1.m1adec
Property / Symbols used
 
Property / Symbols used: Q12132 / rank
 
Normal rank
Property / Symbols used: Q12132 / qualifier
 
test:

s ⁡ ( n , k ) Stirling-number-first-kind-S 𝑛 𝑘 {\displaystyle{\displaystyle s\left(\NVar{n},\NVar{k}\right)}}

\Stirlingnumbers@{\NVar{n}}{\NVar{k}}
Property / Symbols used: Q12132 / qualifier
 
xml-id: C26.S8.SS1.p1.m5adec
Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
test:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5aedec
Property / Symbols used
 
Property / Symbols used: Q11169 / rank
 
Normal rank
Property / Symbols used: Q11169 / qualifier
 
test:

⌊ x ⌋ 𝑥 {\displaystyle{\displaystyle\left\lfloor\NVar{x}\right\rfloor}}

\floor{\NVar{x}}
Property / Symbols used: Q11169 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r17.m4adec
Property / Symbols used
 
Property / Symbols used: Q12113 / rank
 
Normal rank
Property / Symbols used: Q12113 / qualifier
 
test:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q12113 / qualifier
 
xml-id: C24.S1.XMD2.m1dec
Property / Symbols used
 
Property / Symbols used: Q12110 / rank
 
Normal rank
Property / Symbols used: Q12110 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12110 / qualifier
 
xml-id: C24.S1.XMD5.m1gdec
Property / Symbols used
 
Property / Symbols used: Q12137 / rank
 
Normal rank
Property / Symbols used: Q12137 / qualifier
 
test:

β n ⁢ ( λ ) subscript 𝛽 𝑛 𝜆 {\displaystyle{\displaystyle\beta_{n}(\lambda)}}

\beta_{n}(\lambda)
Property / Symbols used: Q12137 / qualifier
 
xml-id: C24.S16.XMD2.m1adec

Latest revision as of 00:51, 2 January 2020

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DLMF:24.16.E8
No description defined

    Statements

    test
    β n ⁢ ( λ ) = n ! ⁢ b n ⁢ λ n + ∑ k = 1 ⌊ n / 2 ⌋ n 2 ⁢ k ⁢ B 2 ⁢ k ⁢ s ⁡ ( n - 1 , 2 ⁢ k - 1 ) ⁢ λ n - 2 ⁢ k , subscript 𝛽 𝑛 𝜆 𝑛 subscript 𝑏 𝑛 superscript 𝜆 𝑛 superscript subscript 𝑘 1 𝑛 2 𝑛 2 𝑘 Bernoulli-number-B 2 𝑘 Stirling-number-first-kind-S 𝑛 1 2 𝑘 1 superscript 𝜆 𝑛 2 𝑘 {\displaystyle{\displaystyle\beta_{n}(\lambda)=n!b_{n}\lambda^{n}+\sum_{k=1}^{% \left\lfloor\ifrac{n}{2}\right\rfloor}\frac{n}{2k}B_{2k}s\left(n-1,2k-1\right)% \lambda^{n-2k},}}
    0 references
    DLMF id
    DLMF:24.16.E8
    0 references
    constraint
    n = 2 , 3 , … 𝑛 2 3 … {\displaystyle{\displaystyle n=2,3,\dots}}
    0 references
    Symbols used
    Q11109
    test
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1adec
    0 references
    Q12132
    test
    s ⁡ ( n , k ) Stirling-number-first-kind-S 𝑛 𝑘 {\displaystyle{\displaystyle s\left(\NVar{n},\NVar{k}\right)}}
    xml-id
    C26.S8.SS1.p1.m5adec
    0 references
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aedec
    0 references
    Q11169
    test
    ⌊ x ⌋ 𝑥 {\displaystyle{\displaystyle\left\lfloor\NVar{x}\right\rfloor}}
    xml-id
    introduction.Sx4.p1.t1.r17.m4adec
    0 references
    Q12113
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C24.S1.XMD2.m1dec
    0 references
    Q12110
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1gdec
    0 references
    Q12137
    test
    β n ⁢ ( λ ) subscript 𝛽 𝑛 𝜆 {\displaystyle{\displaystyle\beta_{n}(\lambda)}}
    xml-id
    C24.S16.XMD2.m1adec
    0 references
     
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