DLMF:1.8.E14 (Q268): 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: 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.m2acdec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
Defining formula:

{\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3ahdec
Property / Symbols used
 
Property / Symbols used: Q10757 / rank
 
Normal rank
Property / Symbols used: Q10757 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q10757 / qualifier
 
xml-id: C1.S1.XMD7.m1kdec

Latest revision as of 16:04, 1 January 2020

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DLMF:1.8.E14
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    Statements

    n = - f ( x + n ) = n = - e 2 π i n x - f ( t ) e - 2 π i n t d t . subscript superscript 𝑛 𝑓 𝑥 𝑛 subscript superscript 𝑛 superscript 𝑒 2 𝜋 𝑖 𝑛 𝑥 subscript superscript 𝑓 𝑡 superscript 𝑒 2 𝜋 𝑖 𝑛 𝑡 𝑡 {\displaystyle{\displaystyle\sum^{\infty}_{n=-\infty}f(x+n)=\sum^{\infty}_{n=-% \infty}e^{2\pi inx}\int^{\infty}_{-\infty}f(t)e^{-2\pi int}\mathrm{d}t.}}
    0 references
    DLMF:1.8.E14
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2ahdec
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1ahdec
    0 references
    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2acdec
    0 references
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2acdec
    0 references
    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3ahdec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C1.S1.XMD7.m1kdec
    0 references