DLMF:24.10.E7 (Q7513): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12123 / rank
 
Normal rank
Property / Symbols used: Q12123 / qualifier
 
Defining formula:

M 𝑀 {\displaystyle{\displaystyle M}}

M
Property / Symbols used: Q12123 / qualifier
 
xml-id: C24.S10.XMD1.m1dec
Property / Symbols used
 
Property / Symbols used: Q12124 / rank
 
Normal rank
Property / Symbols used: Q12124 / qualifier
 
Defining formula:

b 𝑏 {\displaystyle{\displaystyle b}}

b
Property / Symbols used: Q12124 / qualifier
 
xml-id: C24.S10.XMD2.m1dec

Latest revision as of 01:40, 2 January 2020

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DLMF:24.10.E7
No description defined

    Statements

    Defining formula
    ( b 2 ⁢ n - 1 ) ⁢ N 2 ⁢ n ≡ 2 ⁢ n ⁢ b 2 ⁢ n - 1 ⁢ D 2 ⁢ n ⁢ ∑ k = 1 M - 1 k 2 ⁢ n - 1 ⁢ ⌊ k ⁢ b M ⌋ ( mod M ) , modular-equivalence superscript 𝑏 2 𝑛 1 subscript 𝑁 2 𝑛 annotated 2 𝑛 superscript 𝑏 2 𝑛 1 subscript 𝐷 2 𝑛 superscript subscript 𝑘 1 𝑀 1 superscript 𝑘 2 𝑛 1 𝑘 𝑏 𝑀 pmod 𝑀 {\displaystyle{\displaystyle(b^{2n}-1)N_{2n}\equiv{2nb^{2n-1}D_{2n}\sum_{k=1}^% {M-1}k^{2n-1}\left\lfloor\frac{kb}{M}\right\rfloor\pmod{M}},}}
    0 references
    DLMF id
    DLMF:24.10.E7
    0 references
    Symbols used
    Q11169
    Defining formula
    ⌊ x ⌋ 𝑥 {\displaystyle{\displaystyle\left\lfloor\NVar{x}\right\rfloor}}
    xml-id
    introduction.Sx4.p1.t1.r17.m4adec
    0 references
    Q12121
    Defining formula
    ≡ modular-equivalence {\displaystyle{\displaystyle\equiv}}
    xml-id
    introduction.Sx4.p2.t1.r10.m10aedec
    0 references
    Q12113
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C24.S1.XMD2.m1dec
    0 references
    Q12110
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1fdec
    0 references
    Q12123
    Defining formula
    M 𝑀 {\displaystyle{\displaystyle M}}
    xml-id
    C24.S10.XMD1.m1dec
    0 references
    Q12124
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C24.S10.XMD2.m1dec
    0 references
     
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