DLMF:36.12.E11 (Q10003): Difference between revisions
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Changed an Item: Add constraint |
Changed an Item: Add constraint |
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(6 intermediate revisions by the same user not shown) | |||
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.m2adec | |||
Property / Symbols used | |||
Property / Symbols used: exponential function / rank | |||
Normal rank | |||
Property / Symbols used: exponential function / qualifier | |||
Defining formula: 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 | |||
Defining formula: 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 | |||
Defining formula: 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 | |||
Defining formula: 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 | |||
Defining formula: 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 | |||
Defining formula: 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
No description defined
Language | Label | Description | Also known as |
---|---|---|---|
English | DLMF:36.12.E11 |
No description defined |
Statements
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:36.12.E11
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Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryAi@{\NVar{z}}}
C9.S2.SS1.m1adec
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Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \bigO@{\NVar{x}}}
C2.S1.E3.m2aadec
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Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cpi}
C3.S12.E1.m2adec
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Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \exp@@{\NVar{z}}}
C4.S2.E19.m2abdec
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Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \iunit}
C1.S9.E1.m2abdec
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Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle y}
C36.S1.XMD10.m1dec
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Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k}
C36.S1.XMD4.m1cdec
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Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle I(\mathbf{y},k)}
C36.S12.XMD1.m1bdec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f(u,\mathbf{y})}
C36.S12.XMD3.m1fdec
0 references