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DLMF:24.15.E10 - MaRDI portal

DLMF:24.15.E10 (Q8260)

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DLMF:24.15.E10
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    Statements

    DLMF defining formula
    2 ⁢ n - 1 4 ⁢ n ⁢ p 2 ⁢ B 2 ⁢ n ≡ S ⁡ ( p + 2 ⁢ n , p - 1 ) ( mod p 3 ) , modular-equivalence 2 𝑛 1 4 𝑛 superscript 𝑝 2 Bernoulli-number-B 2 𝑛 annotated Stirling-number-second-kind-S 𝑝 2 𝑛 𝑝 1 pmod superscript 𝑝 3 {\displaystyle{\displaystyle\frac{2n-1}{4n}p^{2}B_{2n}\equiv{S\left(p+2n,p-1% \right)\pmod{p^{3}}},}}
    0 references
    constraint
    2 ≤ 2 ⁢ n ≤ p - 3 2 2 𝑛 𝑝 3 {\displaystyle{\displaystyle 2\leq 2n\leq p-3}}
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    Symbols used
    Q11083
    DLMF defining formula
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1afdec
    0 references
    Q12134
    DLMF defining formula
    S ⁡ ( n , k ) Stirling-number-second-kind-S 𝑛 𝑘 {\displaystyle{\displaystyle S\left(\NVar{n},\NVar{k}\right)}}
    xml-id
    C26.S8.SS1.p3.m2acdec
    0 references
    Q12124
    DLMF defining formula
    ≡ modular-equivalence {\displaystyle{\displaystyle\equiv}}
    xml-id
    introduction.Sx4.p2.t1.r10.m10aadec
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    integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1jdec
    0 references
    prime
    DLMF defining formula
    p 𝑝 {\displaystyle{\displaystyle p}}
    xml-id
    C24.S1.XMD8.m1adec
    0 references

    Identifiers

     
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