DLMF:1.17.E8 (Q667): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older edit
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
(One intermediate revision by the same user not shown)
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.m3addec
Property / Symbols used
 
Property / Symbols used: Q10916 / rank
 
Normal rank
Property / Symbols used: Q10916 / qualifier
 
Defining formula:

ϕ ⁢ ( x ) italic-ϕ 𝑥 {\displaystyle{\displaystyle\phi(x)}}

\phi(x)
Property / Symbols used: Q10916 / qualifier
 
xml-id: C1.S17.XMD1.m1ddec

Latest revision as of 16:43, 1 January 2020

No description defined
Language Label Description Also known as
English
DLMF:1.17.E8
No description defined

    Statements

    Defining formula
    1 2 ⁢ π ⁢ ∫ - ∞ ∞ e - i ⁢ a ⁢ t ⁢ ( ∫ - ∞ ∞ ϕ ⁢ ( x ) ⁢ e i ⁢ t ⁢ x ⁢ d x ) ⁢ d t = ϕ ⁢ ( a ) 1 2 𝜋 superscript subscript superscript 𝑒 𝑖 𝑎 𝑡 superscript subscript italic-ϕ 𝑥 superscript 𝑒 𝑖 𝑡 𝑥 𝑥 𝑡 italic-ϕ 𝑎 {\displaystyle{\displaystyle\frac{1}{2\pi}\int_{-\infty}^{\infty}e^{-iat}\left% (\int_{-\infty}^{\infty}\phi(x)e^{itx}\mathrm{d}x\right)\mathrm{d}t=\phi(a)}}
    0 references
    DLMF id
    DLMF:1.17.E8
    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.m2acdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1addec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2acdec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3addec
    0 references
    Q10916
    Defining formula
    ϕ ⁢ ( x ) italic-ϕ 𝑥 {\displaystyle{\displaystyle\phi(x)}}
    xml-id
    C1.S17.XMD1.m1ddec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q667&oldid=23858"