DLMF:1.17.E10 (Q669): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
Defining formula:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1afdec

Revision as of 16:43, 1 January 2020

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DLMF:1.17.E10
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    Statements

    Defining formula
    1 2 ⁢ π ⁢ ∫ - ∞ ∞ e - t 2 / ( 4 ⁢ n ) ⁢ e i ⁢ ( x - a ) ⁢ t ⁢ d t = n π ⁢ e - n ⁢ ( x - a ) 2 . 1 2 𝜋 superscript subscript superscript 𝑒 superscript 𝑡 2 4 𝑛 superscript 𝑒 𝑖 𝑥 𝑎 𝑡 𝑡 𝑛 𝜋 superscript 𝑒 𝑛 superscript 𝑥 𝑎 2 {\displaystyle{\displaystyle\frac{1}{2\pi}\int_{-\infty}^{\infty}e^{-t^{2}/(4n% )}e^{i(x-a)t}\mathrm{d}t=\sqrt{\frac{n}{\pi}}e^{-n(x-a)^{2}}.}}
    0 references
    DLMF id
    DLMF:1.17.E10
    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.m2aedec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1afdec
    0 references
     
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