DLMF:13.23.E9 (Q4643): Difference between revisions

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‎Created a new Item: Wikidata Toolkit example test item creation
 
‎Changed an Item: Add constraint
 
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Property / constraint
 

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\tfrac{1}{2}<\realpart@@{\mu}<\realpart@@{(\kappa+\tfrac{1}{2}\nu)}+\tfrac{3}% {4}}

-\tfrac{1}{2}<\realpart@@{\mu}<\realpart@@{(\kappa+\tfrac{1}{2}\nu)}+\tfrac{3}% {4}
Property / constraint: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\tfrac{1}{2}<\realpart@@{\mu}<\realpart@@{(\kappa+\tfrac{1}{2}\nu)}+\tfrac{3}% {4}} / rank
 
Normal rank
Property / constraint
 

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x>0}

x>0
Property / constraint: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x>0} / rank
 
Normal rank
Property / constraint
 

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\tfrac{1}{2}<\Re\mu<\Re(\kappa+\tfrac{1}{2}\nu)+\tfrac{3}{4}}

-\tfrac{1}{2}<\Re\mu<\Re(\kappa+\tfrac{1}{2}\nu)+\tfrac{3}{4}
Property / constraint: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\tfrac{1}{2}<\Re\mu<\Re(\kappa+\tfrac{1}{2}\nu)+\tfrac{3}{4}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Bessel function of the first kind / rank
 
Normal rank
Property / Symbols used: Bessel function of the first kind / qualifier
 
Defining formula:

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

\BesselJ{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: Bessel function of the first kind / qualifier
 
xml-id: C10.S2.E2.m2adec
Property / Symbols used
 
Property / Symbols used: gamma function / rank
 
Normal rank
Property / Symbols used: gamma function / qualifier
 
Defining formula:

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

\EulerGamma@{\NVar{z}}
Property / Symbols used: gamma function / qualifier
 
xml-id: C5.S2.E1.m2ahdec
Property / Symbols used
 
Property / Symbols used: Whittaker confluent hypergeometric function / rank
 
Normal rank
Property / Symbols used: Whittaker confluent hypergeometric function / qualifier
 
Defining formula:

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

\WhittakerconfhyperM{\NVar{\kappa}}{\NVar{\mu}}@{\NVar{z}}
Property / Symbols used: Whittaker confluent hypergeometric function / qualifier
 
xml-id: C13.S14.E2.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.m1ahdec
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
Defining formula:

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

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2ahdec
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.m3ahdec
Property / Symbols used
 
Property / Symbols used: Q10811 / rank
 
Normal rank
Property / Symbols used: Q10811 / qualifier
 
Defining formula:

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

\realpart@@
Property / Symbols used: Q10811 / qualifier
 
xml-id: C1.S9.E2.m1ahdec
Property / Symbols used
 
Property / Symbols used: Q11566 / rank
 
Normal rank
Property / Symbols used: Q11566 / qualifier
 
Defining formula:

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

x
Property / Symbols used: Q11566 / qualifier
 
xml-id: C13.S1.XMD4.m1adec

Latest revision as of 01:03, 2 January 2020

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DLMF:13.23.E9
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    Statements

    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-\frac{1}{2}t}t^{\mu-\frac{1}{2}(\nu+1)}\WhittakerconfhyperM{\kappa}{\mu}@{t}\BesselJ{\nu}@{2\sqrt{xt}}\diff{t}=\frac{\EulerGamma@{1+2\mu}}{\EulerGamma@{\frac{1}{2}-\mu+\kappa+\nu}}\*e^{-\frac{1}{2}x}x^{\frac{1}{2}(\kappa-\mu-\frac{3}{2})}\*\WhittakerconfhyperM{\frac{1}{2}(\kappa+3\mu-\nu+\frac{1}{2})}{\frac{1}{2}(\kappa-\mu+\nu-\frac{1}{2})}@{x},}
    0 references
    DLMF id
    DLMF:13.23.E9
    0 references
    constraint
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\tfrac{1}{2}<\realpart@@{\mu}<\realpart@@{(\kappa+\tfrac{1}{2}\nu)}+\tfrac{3}% {4}}
    0 references
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x>0}
    0 references
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\tfrac{1}{2}<\Re\mu<\Re(\kappa+\tfrac{1}{2}\nu)+\tfrac{3}{4}}
    0 references
    Symbols used
    Bessel function of the first kind
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\NVar{\nu}}@{\NVar{z}}}
    xml-id
    C10.S2.E2.m2adec
    0 references
    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.m2ahdec
    0 references
    Whittaker confluent hypergeometric function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \WhittakerconfhyperM{\NVar{\kappa}}{\NVar{\mu}}@{\NVar{z}}}
    xml-id
    C13.S14.E2.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.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
    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
    Q10811
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@}
    xml-id
    C1.S9.E2.m1ahdec
    0 references
    Q11566
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x}
    xml-id
    C13.S1.XMD4.m1adec
    0 references
     
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