DLMF:25.15.E6 (Q7751): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
(3 intermediate revisions by the same user not shown)
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
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
Defining formula:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2aadec
Property / Symbols used
 
Property / Symbols used: Q12150 / rank
 
Normal rank
Property / Symbols used: Q12150 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q12150 / qualifier
 
xml-id: C25.S1.XMD1.m1cdec
Property / Symbols used
 
Property / Symbols used: Q12168 / rank
 
Normal rank
Property / Symbols used: Q12168 / qualifier
 
Defining formula:

χ ( n ) 𝜒 𝑛 {\displaystyle{\displaystyle\chi(n)}}

\chi(n)
Property / Symbols used: Q12168 / qualifier
 
xml-id: C25.S15.XMD1.m1edec

Latest revision as of 01:05, 2 January 2020

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English
DLMF:25.15.E6
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    Statements

    G ( χ ) r = 1 k χ ( r ) e 2 π i r / k . equal-by definition 𝐺 𝜒 superscript subscript 𝑟 1 𝑘 𝜒 𝑟 superscript 𝑒 2 𝜋 𝑖 𝑟 𝑘 {\displaystyle{\displaystyle G(\chi)\equiv\sum_{r=1}^{k}\chi(r)e^{2\pi ir/k}.}}
    0 references
    DLMF:25.15.E6
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aadec
    0 references
    equal-by definition {\displaystyle{\displaystyle\equiv}}
    introduction.Sx4.p1.t1.r9.m2adec
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    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2aadec
    0 references
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2aadec
    0 references
    k 𝑘 {\displaystyle{\displaystyle k}}
    C25.S1.XMD1.m1cdec
    0 references
    χ ( n ) 𝜒 𝑛 {\displaystyle{\displaystyle\chi(n)}}
    C25.S15.XMD1.m1edec
    0 references