DLMF:36.12.E3 (Q9994): Difference between revisions

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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.m1adec
Property / Symbols used
 
Property / Symbols used: Q12743 / rank
 
Normal rank
Property / Symbols used: Q12743 / qualifier
 
test:

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

K
Property / Symbols used: Q12743 / qualifier
 
xml-id: C36.S1.XMD7.m1dec
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.m1adec
Property / Symbols used
 
Property / Symbols used: function (locally) / rank
 
Normal rank
Property / Symbols used: function (locally) / qualifier
 
test:

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

a_{m}(\mathbf{y})
Property / Symbols used: function (locally) / qualifier
 
xml-id: C36.S12.XMD10.m1dec
Property / Symbols used
 
Property / Symbols used: function (locally) / rank
 
Normal rank
Property / Symbols used: function (locally) / qualifier
 
test:

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

A(\mathbf{y})
Property / Symbols used: function (locally) / qualifier
 
xml-id: C36.S12.XMD7.m1dec
Property / Symbols used
 
Property / Symbols used: Q12761 / rank
 
Normal rank
Property / Symbols used: Q12761 / qualifier
 
test:

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

\mathbf{z}(\mathbf{y},k)
Property / Symbols used: Q12761 / qualifier
 
xml-id: C36.S12.XMD8.m1dec
Property / Symbols used
 
Property / Symbols used: Q12762 / rank
 
Normal rank
Property / Symbols used: Q12762 / qualifier
 
test:

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

z_{m}(\mathbf{y},k)
Property / Symbols used: Q12762 / qualifier
 
xml-id: C36.S12.XMD9.m1dec

Latest revision as of 15:19, 2 January 2020

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DLMF:36.12.E3
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    Statements

    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle I(\mathbf{y},k)=\frac{\exp@{ikA(\mathbf{y})}}{k^{1/(K+2)}}\sum\limits_{m=0}^{K}\frac{a_{m}(\mathbf{y})}{k^{m/(K+2)}}\left(\Kroneckerdelta{m}{0}-\left(1-\Kroneckerdelta{m}{0}\right)i\pderiv{}{z_{m}}\right)\canonint{K}@{\mathbf{z}(\mathbf{y};k)}\left(1+\bigO@{\frac{1}{k}}\right),}
    0 references
    DLMF id
    DLMF:36.12.E3
    0 references
    Symbols used
    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.m2adec
    0 references
    Q10768
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kroneckerdelta{\NVar{j}}{\NVar{k}}}
    xml-id
    introduction.Sx4.p1.t1.r4.m5adec
    0 references
    canonical integral function
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \canonint{\NVar{K}}@{\NVar{\mathbf{x}}}}
    xml-id
    C36.S2.E4.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.m2aadec
    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.m2aadec
    0 references
    partial derivative of $$f$$ with respect to $$x$$
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{\NVar{f}}{\NVar{x}}}
    xml-id
    C1.S5.E3.m4aadec
    0 references
    partial differential of $$x$$
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pdiff{\NVar{x}}}
    xml-id
    C1.S5.E3.m2aadec
    0 references
    Q12741
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle n}
    xml-id
    C36.S1.XMD2.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.m1adec
    0 references
    Q12743
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle K}
    xml-id
    C36.S1.XMD7.m1dec
    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.m1adec
    0 references
    function (locally)
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{m}(\mathbf{y})}
    xml-id
    C36.S12.XMD10.m1dec
    0 references
    function (locally)
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A(\mathbf{y})}
    xml-id
    C36.S12.XMD7.m1dec
    0 references
    Q12761
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathbf{z}(\mathbf{y},k)}
    xml-id
    C36.S12.XMD8.m1dec
    0 references
    Q12762
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{m}(\mathbf{y},k)}
    xml-id
    C36.S12.XMD9.m1dec
    0 references
     
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