DLMF:1.16.E51 (Q659): 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: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cpi}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2aldec
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \diff{\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1ajdec
Property / Symbols used
 
Property / Symbols used: Q10905 / rank
 
Normal rank
Property / Symbols used: Q10905 / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \intinnerprod{\NVar{\Lambda}}{\NVar{\phi}}}

\intinnerprod{\NVar{\Lambda}}{\NVar{\phi}}
Property / Symbols used: Q10905 / qualifier
 
xml-id: C1.S16.SS1.p5.m5asdec
Property / Symbols used
 
Property / Symbols used: Fourier transform of a tempered distribution / rank
 
Normal rank
Property / Symbols used: Fourier transform of a tempered distribution / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Fouriertransdist@{\NVar{u}}}

\Fouriertransdist@{\NVar{u}}
Property / Symbols used: Fourier transform of a tempered distribution / qualifier
 
xml-id: C1.S16.E35.m2aldec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \iunit}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2aldec
Property / Symbols used
 
Property / Symbols used: Cauchy principal value / rank
 
Normal rank
Property / Symbols used: Cauchy principal value / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pvint_{\NVar{a}}^{\NVar{b}}}

\pvint_{\NVar{a}}^{\NVar{b}}
Property / Symbols used: Cauchy principal value / qualifier
 
xml-id: C1.S4.E24.m2aadec
Property / Symbols used
 
Property / Symbols used: Q10910 / rank
 
Normal rank
Property / Symbols used: Q10910 / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phi(x)}

\phi(x)
Property / Symbols used: Q10910 / qualifier
 
xml-id: C1.S16.XMD7.m1edec

Latest revision as of 15:42, 1 January 2020

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DLMF:1.16.E51
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    Statements

    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \intinnerprod{\Fouriertransdist@{\HeavisideH}}{\phi}=\sqrt{\frac{\cpi}{2}}\phi(0)+\frac{\iunit}{\sqrt{2\cpi}}\pvint^{\infty}_{-\infty}\frac{\phi(x)}{x}\diff{x}.}
    0 references
    DLMF id
    DLMF:1.16.E51
    0 references
    Symbols used
    Heaviside function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \HeavisideH@{\NVar{x}}}
    xml-id
    C1.S16.E13.m2ajdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cpi}
    xml-id
    C3.S12.E1.m2aldec
    0 references
    Q10770
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \diff{\NVar{x}}}
    xml-id
    C1.S4.SS4.m1ajdec
    0 references
    Q10905
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \intinnerprod{\NVar{\Lambda}}{\NVar{\phi}}}
    xml-id
    C1.S16.SS1.p5.m5asdec
    0 references
    Fourier transform of a tempered distribution
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Fouriertransdist@{\NVar{u}}}
    xml-id
    C1.S16.E35.m2aldec
    0 references
    imaginary unit
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \iunit}
    xml-id
    C1.S9.E1.m2aldec
    0 references
    Cauchy principal value
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pvint_{\NVar{a}}^{\NVar{b}}}
    xml-id
    C1.S4.E24.m2aadec
    0 references
    Q10910
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phi(x)}
    xml-id
    C1.S16.XMD7.m1edec
    0 references
     
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