DLMF:15.6.E6 (Q5044): 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.m2aedec
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.m1aedec
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.m2addec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
Defining formula:

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

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3aedec
Property / Symbols used
 
Property / Symbols used: Q10817 / rank
 
Normal rank
Property / Symbols used: Q10817 / qualifier
 
Defining formula:

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

\phase
Property / Symbols used: Q10817 / qualifier
 
xml-id: C1.S9.E7.m1aedec
Property / Symbols used
 
Property / Symbols used: $$={{}_{2}{\mathbf{F}}_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Olver’s hypergeometric function / rank
 
Normal rank
Property / Symbols used: $$={{}_{2}{\mathbf{F}}_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Olver’s hypergeometric function / qualifier
 
Defining formula:

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

\hyperOlverF@{\NVar{a}}{\NVar{b}}{\NVar{c}}{\NVar{z}}
Property / Symbols used: $$={{}_{2}{\mathbf{F}}_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Olver’s hypergeometric function / qualifier
 
xml-id: C15.S2.E2.m2aedec
Property / Symbols used
 
Property / Symbols used: Q11644 / rank
 
Normal rank
Property / Symbols used: Q11644 / qualifier
 
Defining formula:

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

z
Property / Symbols used: Q11644 / qualifier
 
xml-id: C15.S1.XMD3.m1edec
Property / Symbols used
 
Property / Symbols used: Q11645 / rank
 
Normal rank
Property / Symbols used: Q11645 / qualifier
 
Defining formula:

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

a
Property / Symbols used: Q11645 / qualifier
 
xml-id: C15.S1.XMD4.m1edec
Property / Symbols used
 
Property / Symbols used: Q11646 / rank
 
Normal rank
Property / Symbols used: Q11646 / qualifier
 
Defining formula:

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

b
Property / Symbols used: Q11646 / qualifier
 
xml-id: C15.S1.XMD5.m1edec
Property / Symbols used
 
Property / Symbols used: Q11647 / rank
 
Normal rank
Property / Symbols used: Q11647 / qualifier
 
Defining formula:

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

c
Property / Symbols used: Q11647 / qualifier
 
xml-id: C15.S1.XMD6.m1edec

Latest revision as of 13:58, 2 January 2020

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DLMF:15.6.E6
No description defined

    Statements

    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperOlverF@{a}{b}{c}{z}=\frac{1}{2\pi\iunit\EulerGamma@{a}\EulerGamma@{b}}\int_{-\iunit\infty}^{\iunit\infty}\frac{\EulerGamma@{a+t}\EulerGamma@{b+t}\EulerGamma@{-t}}{\EulerGamma@{c+t}}(-z)^{t}\diff{t},}
    0 references
    DLMF id
    DLMF:15.6.E6
    0 references
    constraint
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\phase@{-z}|<\cpi}
    0 references
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\operatorname{ph}\left(-z\right)|<\pi}
    0 references
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a,b\neq 0,-1,-2,\dots}
    0 references
    Symbols used
    gamma function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulerGamma@{\NVar{z}}}
    xml-id
    C5.S2.E1.m2aedec
    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.m2aedec
    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.m1aedec
    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.m2addec
    0 references
    Q10771
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int}
    xml-id
    C1.S4.SS4.m3aedec
    0 references
    Q10817
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phase}
    xml-id
    C1.S9.E7.m1aedec
    0 references
    $$={{}_{2}{\mathbf{F}}_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Olver’s hypergeometric function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperOlverF@{\NVar{a}}{\NVar{b}}{\NVar{c}}{\NVar{z}}}
    xml-id
    C15.S2.E2.m2aedec
    0 references
    Q11644
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z}
    xml-id
    C15.S1.XMD3.m1edec
    0 references
    Q11645
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a}
    xml-id
    C15.S1.XMD4.m1edec
    0 references
    Q11646
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b}
    xml-id
    C15.S1.XMD5.m1edec
    0 references
    Q11647
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c}
    xml-id
    C15.S1.XMD6.m1edec
    0 references
     
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