DLMF:26.10.E18 (Q7901)

From DRMF
Revision as of 14:02, 2 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
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
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q7901&oldid=42731"