DLMF:25.13.E1 (Q7737): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: Q12148 / rank
 
Normal rank
Property / Symbols used: Q12148 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12148 / qualifier
 
xml-id: C25.S1.XMD3.m1dec
Property / Symbols used
 
Property / Symbols used: Q12152 / rank
 
Normal rank
Property / Symbols used: Q12152 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q12152 / qualifier
 
xml-id: C25.S1.XMD5.m1dec
Property / Symbols used
 
Property / Symbols used: Q12149 / rank
 
Normal rank
Property / Symbols used: Q12149 / qualifier
 
Defining formula:

s 𝑠 {\displaystyle{\displaystyle s}}

s
Property / Symbols used: Q12149 / qualifier
 
xml-id: C25.S1.XMD7.m1dec

Latest revision as of 13:50, 2 January 2020

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English
DLMF:25.13.E1
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    Statements

    F ( x , s ) n = 1 e 2 π i n x n s , equal-by definition periodic-zeta 𝑥 𝑠 superscript subscript 𝑛 1 superscript 𝑒 2 𝜋 𝑖 𝑛 𝑥 superscript 𝑛 𝑠 {\displaystyle{\displaystyle F\left(x,s\right)\equiv\sum_{n=1}^{\infty}\frac{e% ^{2\pi inx}}{n^{s}},}}
    0 references
    DLMF:25.13.E1
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2adec
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    equal-by definition {\displaystyle{\displaystyle\equiv}}
    introduction.Sx4.p1.t1.r9.m2adec
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    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2adec
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    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2adec
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    n 𝑛 {\displaystyle{\displaystyle n}}
    C25.S1.XMD3.m1dec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C25.S1.XMD5.m1dec
    0 references
    s 𝑠 {\displaystyle{\displaystyle s}}
    C25.S1.XMD7.m1dec
    0 references