DLMF:36.12.E11 (Q10003): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: exponential function / rank
 
Normal rank
Property / Symbols used: exponential function / qualifier
 
test:

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

\exp@@{\NVar{z}}
Property / Symbols used: exponential function / qualifier
 
xml-id: C4.S2.E19.m2abdec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
test:

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.m2abdec
Property / Symbols used
 
Property / Symbols used: Q12745 / rank
 
Normal rank
Property / Symbols used: Q12745 / qualifier
 
test:

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

y
Property / Symbols used: Q12745 / qualifier
 
xml-id: C36.S1.XMD10.m1dec
Property / Symbols used
 
Property / Symbols used: Q12750 / rank
 
Normal rank
Property / Symbols used: Q12750 / qualifier
 
test:

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

k
Property / Symbols used: Q12750 / qualifier
 
xml-id: C36.S1.XMD4.m1cdec
Property / Symbols used
 
Property / Symbols used: oscillatory integral (locally) / rank
 
Normal rank
Property / Symbols used: oscillatory integral (locally) / qualifier
 
test:

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

I(\mathbf{y},k)
Property / Symbols used: oscillatory integral (locally) / qualifier
 
xml-id: C36.S12.XMD1.m1bdec
Property / Symbols used
 
Property / Symbols used: Q12760 / rank
 
Normal rank
Property / Symbols used: Q12760 / qualifier
 
test:

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

f(u,\mathbf{y})
Property / Symbols used: Q12760 / qualifier
 
xml-id: C36.S12.XMD3.m1fdec

Latest revision as of 15:21, 2 January 2020

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DLMF:36.12.E11
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    Statements

    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle I(y,k)=\frac{\Delta^{1/4}\pi\sqrt{2}}{k^{1/3}}\exp@{ik\widetilde{f}}\left(\left(\frac{g_{+}}{\sqrt{f_{+}^{\prime\prime}}}+\frac{g_{-}}{\sqrt{-f_{-}^{\prime\prime}}}\right)\AiryAi@{-k^{2/3}\Delta}\left(1+\bigO@{\frac{1}{k}}\right)-i\left(\frac{g_{+}}{\sqrt{f_{+}^{\prime\prime}}}-\frac{g_{-}}{\sqrt{-f_{-}^{\prime\prime}}}\right)\frac{\AiryAi'@{-k^{2/3}\Delta}}{k^{1/3}\Delta^{1/2}}\left(1+\bigO@{\frac{1}{k}}\right)\right),}
    0 references
    DLMF id
    DLMF:36.12.E11
    0 references
    Symbols used
    Q10919
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryAi@{\NVar{z}}}
    xml-id
    C9.S2.SS1.m1adec
    0 references
    order not exceeding
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \bigO@{\NVar{x}}}
    xml-id
    C2.S1.E3.m2aadec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cpi}
    xml-id
    C3.S12.E1.m2adec
    0 references
    exponential function
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \exp@@{\NVar{z}}}
    xml-id
    C4.S2.E19.m2abdec
    0 references
    imaginary unit
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \iunit}
    xml-id
    C1.S9.E1.m2abdec
    0 references
    Q12745
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle y}
    xml-id
    C36.S1.XMD10.m1dec
    0 references
    Q12750
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k}
    xml-id
    C36.S1.XMD4.m1cdec
    0 references
    oscillatory integral (locally)
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle I(\mathbf{y},k)}
    xml-id
    C36.S12.XMD1.m1bdec
    0 references
    Q12760
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f(u,\mathbf{y})}
    xml-id
    C36.S12.XMD3.m1fdec
    0 references
     
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