DLMF:22.16.E8 (Q7127): Difference between revisions
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Changed an Item: Add constraint |
Changed an Item: Add constraint |
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| (7 intermediate revisions by the same user not shown) | |||
| Property / Symbols used | |||
| Property / Symbols used: Gudermannian function / rank | |||
Normal rank | |||
| Property / Symbols used: Gudermannian function / qualifier | |||
Defining formula: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Gudermannian@@{\NVar{x}}}\Gudermannian@@{\NVar{x}} | |||
| Property / Symbols used: Gudermannian function / qualifier | |||
xml-id: C4.S23.E39.m2aadec | |||
| Property / Symbols used | |||
| Property / Symbols used: Jacobi’s amplitude function / rank | |||
Normal rank | |||
| Property / Symbols used: Jacobi’s amplitude function / qualifier | |||
Defining formula: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiamk@{\NVar{x}}{\NVar{k}}}\Jacobiamk@{\NVar{x}}{\NVar{k}} | |||
| Property / Symbols used: Jacobi’s amplitude function / qualifier | |||
xml-id: C22.S16.E1.m2agdec | |||
| Property / Symbols used | |||
| Property / Symbols used: hyperbolic cosine function / rank | |||
Normal rank | |||
| Property / Symbols used: hyperbolic cosine function / qualifier | |||
Defining formula: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cosh@@{\NVar{z}}}\cosh@@{\NVar{z}} | |||
| Property / Symbols used: hyperbolic cosine function / qualifier | |||
xml-id: C4.S28.E2.m2adec | |||
| Property / Symbols used | |||
| Property / Symbols used: hyperbolic secant function / rank | |||
Normal rank | |||
| Property / Symbols used: hyperbolic secant function / qualifier | |||
Defining formula: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sech@@{\NVar{z}}}\sech@@{\NVar{z}} | |||
| Property / Symbols used: hyperbolic secant function / qualifier | |||
xml-id: C4.S28.E6.m2adec | |||
| Property / Symbols used | |||
| Property / Symbols used: hyperbolic sine function / rank | |||
Normal rank | |||
| Property / Symbols used: hyperbolic sine function / qualifier | |||
Defining formula: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sinh@@{\NVar{z}}}\sinh@@{\NVar{z}} | |||
| Property / Symbols used: hyperbolic sine function / qualifier | |||
xml-id: C4.S28.E1.m2adec | |||
| Property / Symbols used | |||
| Property / Symbols used: Q12003 / rank | |||
Normal rank | |||
| Property / Symbols used: Q12003 / qualifier | |||
Defining formula: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x}x | |||
| Property / Symbols used: Q12003 / qualifier | |||
xml-id: C22.S1.XMD1.m1gdec | |||
| Property / Symbols used | |||
| Property / Symbols used: Q11984 / rank | |||
Normal rank | |||
| Property / Symbols used: Q11984 / qualifier | |||
Defining formula: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k}k | |||
| Property / Symbols used: Q11984 / qualifier | |||
xml-id: C22.S1.XMD4.m1edec | |||
| Property / Symbols used | |||
| Property / Symbols used: Q11988 / rank | |||
Normal rank | |||
| Property / Symbols used: Q11988 / qualifier | |||
Defining formula: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k^{\prime}}k^{\prime} | |||
| Property / Symbols used: Q11988 / qualifier | |||
xml-id: C22.S1.XMD5.m1dec | |||
Latest revision as of 15:31, 2 January 2020
No description defined
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | DLMF:22.16.E8 |
No description defined |
Statements
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiamk@{x}{k}=\Gudermannian@@{x}-\tfrac{1}{4}{k^{\prime}}^{2}(x-\sinh@@{x}\cosh@@{x})\sech@@{x}+\bigO\left({k^{\prime}}^{4}\right).}
0 references
DLMF:22.16.E8
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \bigO@{\NVar{x}}}
C2.S1.E3.m2abdec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Gudermannian@@{\NVar{x}}}
C4.S23.E39.m2aadec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiamk@{\NVar{x}}{\NVar{k}}}
C22.S16.E1.m2agdec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cosh@@{\NVar{z}}}
C4.S28.E2.m2adec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sech@@{\NVar{z}}}
C4.S28.E6.m2adec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sinh@@{\NVar{z}}}
C4.S28.E1.m2adec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x}
C22.S1.XMD1.m1gdec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k}
C22.S1.XMD4.m1edec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k^{\prime}}
C22.S1.XMD5.m1dec
0 references