DLMF:4.23.E40 (Q1792): Difference between revisions

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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 cotangent function / rank
 
Normal rank
Property / Symbols used: hyperbolic cotangent function / qualifier
 
Defining formula:

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

\coth@@{\NVar{z}}
Property / Symbols used: hyperbolic cotangent function / qualifier
 
xml-id: C4.S28.E7.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.m2aadec
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: hyperbolic tangent function / rank
 
Normal rank
Property / Symbols used: hyperbolic tangent function / qualifier
 
Defining formula:

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

\tanh@@{\NVar{z}}
Property / Symbols used: hyperbolic tangent function / qualifier
 
xml-id: C4.S28.E4.m2adec
Property / Symbols used
 
Property / Symbols used: arccosecant function / rank
 
Normal rank
Property / Symbols used: arccosecant function / qualifier
 
Defining formula:

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

\acsc@@{\NVar{z}}
Property / Symbols used: arccosecant function / qualifier
 
xml-id: C4.S23.E7.m2aedec
Property / Symbols used
 
Property / Symbols used: Q11208 / rank
 
Normal rank
Property / Symbols used: Q11208 / qualifier
 
Defining formula:

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

\acos@@{\NVar{z}}
Property / Symbols used: Q11208 / qualifier
 
xml-id: C4.S23.SS2.p1.m6akdec
Property / Symbols used
 
Property / Symbols used: arccotangent function / rank
 
Normal rank
Property / Symbols used: arccotangent function / qualifier
 
Defining formula:

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

\acot@@{\NVar{z}}
Property / Symbols used: arccotangent function / qualifier
 
xml-id: C4.S23.E9.m2aedec
Property / Symbols used
 
Property / Symbols used: arcsecant function / rank
 
Normal rank
Property / Symbols used: arcsecant function / qualifier
 
Defining formula:

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

\asec@@{\NVar{z}}
Property / Symbols used: arcsecant function / qualifier
 
xml-id: C4.S23.E8.m2aedec
Property / Symbols used
 
Property / Symbols used: Q11242 / rank
 
Normal rank
Property / Symbols used: Q11242 / qualifier
 
Defining formula:

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

\asin@@{\NVar{z}}
Property / Symbols used: Q11242 / qualifier
 
xml-id: C4.S23.SS2.p1.m5ajdec
Property / Symbols used
 
Property / Symbols used: Q10816 / rank
 
Normal rank
Property / Symbols used: Q10816 / qualifier
 
Defining formula:

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

\atan@@{\NVar{z}}
Property / Symbols used: Q10816 / qualifier
 
xml-id: C4.S23.SS2.p1.m7aidec
Property / Symbols used
 
Property / Symbols used: Q11218 / rank
 
Normal rank
Property / Symbols used: Q11218 / qualifier
 
Defining formula:

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

x
Property / Symbols used: Q11218 / qualifier
 
xml-id: C4.S1.XMD6.m1kdec

Latest revision as of 18:36, 1 January 2020

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DLMF:4.23.E40
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    Statements

    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Gudermannian@{x}=2\atan@{e^{x}}-\tfrac{1}{2}\pi\\ =\asin@{\tanh@@{x}}=\acsc@{\coth@@{x}}\\ =\acos@{\sech@@{x}}=\asec@{\cosh@@{x}}\\ =\atan@{\sinh@@{x}}=\acot@{\csch@@{x}}.}
    0 references
    DLMF id
    DLMF:4.23.E40
    0 references
    Symbols used
    Gudermannian function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Gudermannian@@{\NVar{x}}}
    xml-id
    C4.S23.E39.m2aadec
    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.m2andec
    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.m2adec
    0 references
    hyperbolic cosecant function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \csch@@{\NVar{z}}}
    xml-id
    C4.S28.E5.m2adec
    0 references
    hyperbolic cosine function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cosh@@{\NVar{z}}}
    xml-id
    C4.S28.E2.m2adec
    0 references
    hyperbolic cotangent function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \coth@@{\NVar{z}}}
    xml-id
    C4.S28.E7.m2adec
    0 references
    hyperbolic secant function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sech@@{\NVar{z}}}
    xml-id
    C4.S28.E6.m2aadec
    0 references
    hyperbolic sine function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sinh@@{\NVar{z}}}
    xml-id
    C4.S28.E1.m2adec
    0 references
    hyperbolic tangent function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tanh@@{\NVar{z}}}
    xml-id
    C4.S28.E4.m2adec
    0 references
    arccosecant function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \acsc@@{\NVar{z}}}
    xml-id
    C4.S23.E7.m2aedec
    0 references
    Q11208
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \acos@@{\NVar{z}}}
    xml-id
    C4.S23.SS2.p1.m6akdec
    0 references
    arccotangent function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \acot@@{\NVar{z}}}
    xml-id
    C4.S23.E9.m2aedec
    0 references
    arcsecant function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \asec@@{\NVar{z}}}
    xml-id
    C4.S23.E8.m2aedec
    0 references
    Q11242
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \asin@@{\NVar{z}}}
    xml-id
    C4.S23.SS2.p1.m5ajdec
    0 references
    Q10816
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \atan@@{\NVar{z}}}
    xml-id
    C4.S23.SS2.p1.m7aidec
    0 references
    Q11218
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x}
    xml-id
    C4.S1.XMD6.m1kdec
    0 references
     
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