DLMF:1.15.E36 (Q578): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10899 / rank
Normal rank
 
Property / Symbols used: Q10899 / qualifier
test:

h ⁢ ( x , y ) ℎ 𝑥 𝑦 {\displaystyle{\displaystyle h(x,y)}}

h(x,y)
 
Property / Symbols used: Q10899 / qualifier
xml-id: C1.S15.XMD8.m1dec
 

Latest revision as of 15:31, 1 January 2020

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DLMF:1.15.E36
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    Statements

    test
    h ⁢ ( x , y ) = 1 2 ⁢ π ⁢ ∫ - ∞ ∞ e - y ⁢ | t | ⁢ e - i ⁢ x ⁢ t ⁢ F ⁢ ( t ) ⁢ d t , ℎ 𝑥 𝑦 1 2 𝜋 subscript superscript superscript 𝑒 𝑦 𝑡 superscript 𝑒 𝑖 𝑥 𝑡 𝐹 𝑡 𝑡 {\displaystyle{\displaystyle h(x,y)=\frac{1}{\sqrt{2\pi}}\int^{\infty}_{-% \infty}e^{-y|t|}e^{-ixt}F(t)\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:1.15.E36
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2afdec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1akdec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aidec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2ahdec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3akdec
    0 references
    Q10886
    test
    F ⁢ ( x ) 𝐹 𝑥 {\displaystyle{\displaystyle F(x)}}
    xml-id
    C1.S14.XMD1.m1dec
    0 references
     
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