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

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
Defining formula:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2aadec

Revision as of 14:01, 2 January 2020

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DLMF:26.10.E18
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    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
     
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