DLMF:26.10.E18 (Q7901): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12172 / rank
 
Normal rank
Property / Symbols used: Q12172 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12172 / qualifier
 
xml-id: C26.S1.XMD6.m1qdec
Property / Symbols used
 
Property / Symbols used: Q12195 / rank
 
Normal rank
Property / Symbols used: Q12195 / qualifier
 
Defining formula:

A k ⁢ ( n ) subscript 𝐴 𝑘 𝑛 {\displaystyle{\displaystyle A_{k}(n)}}

A_{k}(n)
Property / Symbols used: Q12195 / qualifier
 
xml-id: C26.S10.XMD4.m1adec
Property / Symbols used
 
Property / Symbols used: function (locally) / rank
 
Normal rank
Property / Symbols used: function (locally) / qualifier
 
Defining formula:

f ⁢ ( h , k ) 𝑓 ℎ 𝑘 {\displaystyle{\displaystyle f(h,k)}}

f(h,k)
Property / Symbols used: function (locally) / qualifier
 
xml-id: C26.S10.XMD5.m1dec

Latest revision as of 14:02, 2 January 2020

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English
DLMF:26.10.E18
No description defined

    Statements

    Defining formula
    A k ⁢ ( n ) = ∑ 1 < h ≤ k ( h , k ) = 1 e π ⁢ i ⁢ f ⁢ ( h , k ) - ( 2 ⁢ π ⁢ i ⁢ n ⁢ h / k ) , subscript 𝐴 𝑘 𝑛 subscript 1 ℎ 𝑘 ℎ 𝑘 1 imaginary-unit 𝑓 ℎ 𝑘 2 imaginary-unit 𝑛 ℎ 𝑘 {\displaystyle{\displaystyle A_{k}(n)=\sum_{\begin{subarray}{c}1<h\leq k\\ \left(h,k\right)=1\end{subarray}}{\mathrm{e}^{\pi\mathrm{i}f(h,k)-(2\pi\mathrm% {i}nh/k)}},}}
    0 references
    DLMF id
    DLMF:26.10.E18
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
    0 references
    Q12093
    Defining formula
    ( m , n ) 𝑚 𝑛 {\displaystyle{\displaystyle\left(\NVar{m},\NVar{n}\right)}}
    xml-id
    C27.S1.p2.t1.r3.m6adec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    Q12186
    Defining formula
    h ℎ {\displaystyle{\displaystyle h}}
    xml-id
    C26.S1.XMD2.m1dec
    0 references
    Q12174
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C26.S1.XMD4.m1hdec
    0 references
    Q12172
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C26.S1.XMD6.m1qdec
    0 references
    Q12195
    Defining formula
    A k ⁢ ( n ) subscript 𝐴 𝑘 𝑛 {\displaystyle{\displaystyle A_{k}(n)}}
    xml-id
    C26.S10.XMD4.m1adec
    0 references
    function (locally)
    Defining formula
    f ⁢ ( h , k ) 𝑓 ℎ 𝑘 {\displaystyle{\displaystyle f(h,k)}}
    xml-id
    C26.S10.XMD5.m1dec
    0 references
     
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