DLMF:9.13.E12 (Q2974): Difference between revisions

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‎Created a new Item: Wikidata Toolkit example test item creation
 
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Property / Symbols used
 
Property / Symbols used: order not exceeding / rank
 
Normal rank
Property / Symbols used: order not exceeding / qualifier
 
Defining formula:

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

\bigO@{\NVar{x}}
Property / Symbols used: order not exceeding / qualifier
 
xml-id: C2.S1.E3.m2acdec
Property / Symbols used
 
Property / Symbols used: Q11417 / rank
 
Normal rank
Property / Symbols used: Q11417 / qualifier
 
Defining formula:

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

\genAiryODEB{\NVar{n}}@{\NVar{z}}
Property / Symbols used: Q11417 / qualifier
 
xml-id: C9.S13.SS1.p2.m4afdec
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: 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.m2acdec
Property / Symbols used
 
Property / Symbols used: Q10901 / rank
 
Normal rank
Property / Symbols used: Q10901 / qualifier
 
Defining formula:

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

\imagpart@@
Property / Symbols used: Q10901 / qualifier
 
xml-id: C1.S9.E2.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.m1acdec
Property / Symbols used
 
Property / Symbols used: sine function / rank
 
Normal rank
Property / Symbols used: sine function / qualifier
 
Defining formula:

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

\sin@@{\NVar{z}}
Property / Symbols used: sine function / qualifier
 
xml-id: C4.S14.E1.m2acdec
Property / Symbols used
 
Property / Symbols used: Q11381 / rank
 
Normal rank
Property / Symbols used: Q11381 / qualifier
 
Defining formula:

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

z
Property / Symbols used: Q11381 / qualifier
 
xml-id: C9.S1.XMD3.m1jdec
Property / Symbols used
 
Property / Symbols used: Q11386 / rank
 
Normal rank
Property / Symbols used: Q11386 / qualifier
 
Defining formula:

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

\delta
Property / Symbols used: Q11386 / qualifier
 
xml-id: C9.S1.XMD4.m1cdec
Property / Symbols used
 
Property / Symbols used: parameter (locally) / rank
 
Normal rank
Property / Symbols used: parameter (locally) / qualifier
 
Defining formula:

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

n
Property / Symbols used: parameter (locally) / qualifier
 
xml-id: C9.S13.XMD1.m1jdec
Property / Symbols used
 
Property / Symbols used: Q11414 / rank
 
Normal rank
Property / Symbols used: Q11414 / qualifier
 
Defining formula:

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

p
Property / Symbols used: Q11414 / qualifier
 
xml-id: C9.S13.XMD3.m1jdec
Property / Symbols used
 
Property / Symbols used: Q11415 / rank
 
Normal rank
Property / Symbols used: Q11415 / qualifier
 
Defining formula:

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

\zeta
Property / Symbols used: Q11415 / qualifier
 
xml-id: C9.S13.XMD4.m1hdec

Latest revision as of 15:01, 2 January 2020

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DLMF:9.13.E12
No description defined

    Statements

    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \genAiryODEB{n}@{-z}=\begin{cases}-(\ifrac{2}{\sqrt{\pi}})\sin@{\tfrac{1}{2}p\pi}z^{-n/4}\left(\sin@{\zeta-\tfrac{1}{4}\pi}+e^{\abs{\imagpart@@{\zeta}}}\bigO@{\zeta^{-1}}\right),&\abs{\phase@@{z}}\leq 2p\pi-\delta,n\text{ odd},\\ (\ifrac{1}{\sqrt{\pi}})\sin@{p\pi}z^{-n/4}e^{-\zeta}\left(1+\bigO@{\zeta^{-1}}\right),&\abs{\phase@@{z}}\leq 3p\pi-\delta,n\text{ even}.\end{cases}}
    0 references
    DLMF id
    DLMF:9.13.E12
    0 references
    Symbols used
    order not exceeding
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \bigO@{\NVar{x}}}
    xml-id
    C2.S1.E3.m2acdec
    0 references
    Q11417
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \genAiryODEB{\NVar{n}}@{\NVar{z}}}
    xml-id
    C9.S13.SS1.p2.m4afdec
    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
    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.m2acdec
    0 references
    Q10901
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \imagpart@@}
    xml-id
    C1.S9.E2.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.m1acdec
    0 references
    sine function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@@{\NVar{z}}}
    xml-id
    C4.S14.E1.m2acdec
    0 references
    Q11381
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z}
    xml-id
    C9.S1.XMD3.m1jdec
    0 references
    Q11386
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \delta}
    xml-id
    C9.S1.XMD4.m1cdec
    0 references
    parameter (locally)
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle n}
    xml-id
    C9.S13.XMD1.m1jdec
    0 references
    Q11414
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p}
    xml-id
    C9.S13.XMD3.m1jdec
    0 references
    Q11415
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \zeta}
    xml-id
    C9.S13.XMD4.m1hdec
    0 references
     
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