DLMF:12.10.E38 (Q4203): Difference between revisions

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‎Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: Q10931 / rank
 
Normal rank
Property / Symbols used: Q10931 / qualifier
 
Defining formula:

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

\asympexp
Property / Symbols used: Q10931 / qualifier
 
xml-id: C2.S1.SS3.p1.m11aqdec
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: 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.m2aedec
Property / Symbols used
 
Property / Symbols used: Q11526 / rank
 
Normal rank
Property / Symbols used: Q11526 / qualifier
 
Defining formula:

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

s
Property / Symbols used: Q11526 / qualifier
 
xml-id: C12.S1.XMD5.m1aadec
Property / Symbols used
 
Property / Symbols used: Q11534 / rank
 
Normal rank
Property / Symbols used: Q11534 / qualifier
 
Defining formula:

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

\zeta
Property / Symbols used: Q11534 / qualifier
 
xml-id: C12.S10.XMD21.m1cdec
Property / Symbols used
 
Property / Symbols used: function (locally) / rank
 
Normal rank
Property / Symbols used: function (locally) / qualifier
 
Defining formula:

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

\phi(\zeta)
Property / Symbols used: function (locally) / qualifier
 
xml-id: C12.S10.XMD22.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11537 / rank
 
Normal rank
Property / Symbols used: Q11537 / qualifier
 
Defining formula:

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

C_{s}(\zeta)
Property / Symbols used: Q11537 / qualifier
 
xml-id: C12.S10.XMD27.m1adec
Property / Symbols used
 
Property / Symbols used: Q11538 / rank
 
Normal rank
Property / Symbols used: Q11538 / qualifier
 
Defining formula:

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

D_{s}(\zeta)
Property / Symbols used: Q11538 / qualifier
 
xml-id: C12.S10.XMD28.m1adec
Property / Symbols used
 
Property / Symbols used: expansion (locally) / rank
 
Normal rank
Property / Symbols used: expansion (locally) / qualifier
 
Defining formula:

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

g(\mu)
Property / Symbols used: expansion (locally) / qualifier
 
xml-id: C12.S10.XMD7.m1ldec

Latest revision as of 14:22, 2 January 2020

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DLMF:12.10.E38
No description defined

    Statements

    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \paraV'@{-\tfrac{1}{2}\mu^{2}}{\mu t\sqrt{2}}\asympexp\frac{(2\pi)^{\frac{1}{2}}\mu^{\frac{2}{3}}g(\mu)}{\phi(\zeta)\EulerGamma@{\tfrac{1}{2}+\tfrac{1}{2}\mu^{2}}}\*\left(\frac{\AiryBi@{\mu^{\frac{4}{3}}\zeta}}{\mu^{\frac{4}{3}}}\sum_{s=0}^{\infty}\frac{C_{s}(\zeta)}{\mu^{4s}}+\AiryBi'@{\mu^{\frac{4}{3}}\zeta}\sum_{s=0}^{\infty}\frac{D_{s}(\zeta)}{\mu^{4s}}\right).}
    0 references
    DLMF id
    DLMF:12.10.E38
    0 references
    Symbols used
    Q11081
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryBi@{\NVar{z}}}
    xml-id
    C9.S2.SS1.m2aadec
    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.m2afdec
    0 references
    Q10931
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \asympexp}
    xml-id
    C2.S1.SS3.p1.m11aqdec
    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
    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.m2aedec
    0 references
    Q11526
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s}
    xml-id
    C12.S1.XMD5.m1aadec
    0 references
    Q11534
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \zeta}
    xml-id
    C12.S10.XMD21.m1cdec
    0 references
    function (locally)
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phi(\zeta)}
    xml-id
    C12.S10.XMD22.m1cdec
    0 references
    Q11537
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle C_{s}(\zeta)}
    xml-id
    C12.S10.XMD27.m1adec
    0 references
    Q11538
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle D_{s}(\zeta)}
    xml-id
    C12.S10.XMD28.m1adec
    0 references
    expansion (locally)
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle g(\mu)}
    xml-id
    C12.S10.XMD7.m1ldec
    0 references
     
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