DLMF:12.5.E9 (Q4123): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older edit
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
(3 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q11517 / rank
 
Normal rank
Property / Symbols used: Q11517 / qualifier
 
Defining formula:

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

\paraV@{\NVar{a}}{\NVar{z}}
Property / Symbols used: Q11517 / qualifier
 
xml-id: C12.S2.SS1.p1.m2aadec
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.m1afdec
Property / Symbols used
 
Property / Symbols used: Q11513 / rank
 
Normal rank
Property / Symbols used: Q11513 / qualifier
 
Defining formula:

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

z
Property / Symbols used: Q11513 / qualifier
 
xml-id: C12.S1.XMD3.m1hdec
Property / Symbols used
 
Property / Symbols used: Q11516 / rank
 
Normal rank
Property / Symbols used: Q11516 / qualifier
 
Defining formula:

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

a
Property / Symbols used: Q11516 / qualifier
 
xml-id: C12.S1.XMD6.m1hdec

Latest revision as of 14:11, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:12.5.E9
No description defined

    Statements

    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraV@{a}{z}=\sqrt{\frac{2}{\pi}}\frac{e^{\frac{1}{4}z^{2}}z^{a-\frac{1}{2}}}{2\pi i\EulerGamma@{\frac{1}{2}-a}}\*\int_{-i\infty}^{i\infty}\EulerGamma@{t}\EulerGamma@{\tfrac{1}{2}-a-2t}2^{t}z^{2t}\cos@{\pi t}\diff{t},}
    0 references
    DLMF id
    DLMF:12.5.E9
    0 references
    constraint
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\phase@@{z}|<\tfrac{1}{4}\pi}
    0 references
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a\neq\frac{1}{2},\frac{3}{2},\frac{5}{2},\dots}
    0 references
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\operatorname{ph}z|<\tfrac{1}{4}\pi}
    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.m2agdec
    0 references
    cosine function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{\NVar{z}}}
    xml-id
    C4.S14.E2.m2aadec
    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.m1ahdec
    0 references
    base of natural logarithm
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \expe}
    xml-id
    C4.S2.E11.m2ahdec
    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.m3ahdec
    0 references
    Q11517
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraV@{\NVar{a}}{\NVar{z}}}
    xml-id
    C12.S2.SS1.p1.m2aadec
    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.m1afdec
    0 references
    Q11513
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z}
    xml-id
    C12.S1.XMD3.m1hdec
    0 references
    Q11516
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a}
    xml-id
    C12.S1.XMD6.m1hdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q4123&oldid=55158"