DLMF:4.23.E42 (Q1794): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: cosine function / rank
 
Normal rank
Property / Symbols used: cosine function / qualifier
 
Defining formula:

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

\cos@@{\NVar{z}}
Property / Symbols used: cosine function / qualifier
 
xml-id: C4.S14.E2.m2aadec
Property / Symbols used
 
Property / Symbols used: cotangent function / rank
 
Normal rank
Property / Symbols used: cotangent function / qualifier
 
Defining formula:

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

\cot@@{\NVar{z}}
Property / Symbols used: cotangent function / qualifier
 
xml-id: C4.S14.E7.m2adec
Property / Symbols used
 
Property / Symbols used: inverse hyperbolic cosecant function / rank
 
Normal rank
Property / Symbols used: inverse hyperbolic cosecant function / qualifier
 
Defining formula:

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

\acsch@@{\NVar{z}}
Property / Symbols used: inverse hyperbolic cosecant function / qualifier
 
xml-id: C4.S37.E7.m2adec
Property / Symbols used
 
Property / Symbols used: Q11246 / rank
 
Normal rank
Property / Symbols used: Q11246 / qualifier
 
Defining formula:

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

\acosh@@{\NVar{z}}
Property / Symbols used: Q11246 / qualifier
 
xml-id: C4.S37.SS2.p1.m9adec
Property / Symbols used
 
Property / Symbols used: inverse hyperbolic cotangent function / rank
 
Normal rank
Property / Symbols used: inverse hyperbolic cotangent function / qualifier
 
Defining formula:

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

\acoth@@{\NVar{z}}
Property / Symbols used: inverse hyperbolic cotangent function / qualifier
 
xml-id: C4.S37.E9.m2adec
Property / Symbols used
 
Property / Symbols used: inverse hyperbolic secant function / rank
 
Normal rank
Property / Symbols used: inverse hyperbolic secant function / qualifier
 
Defining formula:

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

\asech@@{\NVar{z}}
Property / Symbols used: inverse hyperbolic secant function / qualifier
 
xml-id: C4.S37.E8.m2adec
Property / Symbols used
 
Property / Symbols used: Q11247 / rank
 
Normal rank
Property / Symbols used: Q11247 / qualifier
 
Defining formula:

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

\asinh@@{\NVar{z}}
Property / Symbols used: Q11247 / qualifier
 
xml-id: C4.S37.SS2.p1.m8adec
Property / Symbols used
 
Property / Symbols used: Q11248 / rank
 
Normal rank
Property / Symbols used: Q11248 / qualifier
 
Defining formula:

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

\atanh@@{\NVar{z}}
Property / Symbols used: Q11248 / qualifier
 
xml-id: C4.S37.SS2.p1.m10adec
Property / Symbols used
 
Property / Symbols used: inverse Gudermannian function / rank
 
Normal rank
Property / Symbols used: inverse Gudermannian function / qualifier
 
Defining formula:

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

\aGudermannian@{\NVar{x}}
Property / Symbols used: inverse Gudermannian function / qualifier
 
xml-id: C4.S23.E41.m2aadec
Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
Defining formula:

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

\ln@@{\NVar{z}}
Property / Symbols used: principal branch of logarithm function / qualifier
 
xml-id: C4.S2.E2.m2aldec
Property / Symbols used
 
Property / Symbols used: secant function / rank
 
Normal rank
Property / Symbols used: secant function / qualifier
 
Defining formula:

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

\sec@@{\NVar{z}}
Property / Symbols used: secant function / qualifier
 
xml-id: C4.S14.E6.m2aadec
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.m2aadec
Property / Symbols used
 
Property / Symbols used: tangent function / rank
 
Normal rank
Property / Symbols used: tangent function / qualifier
 
Defining formula:

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

\tan@@{\NVar{z}}
Property / Symbols used: tangent function / qualifier
 
xml-id: C4.S14.E4.m2aadec
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.m1mdec

Latest revision as of 17:37, 1 January 2020

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DLMF:4.23.E42
No description defined

    Statements

    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \aGudermannian@{x}=\ln@@{\tan@{\tfrac{1}{2}x+\tfrac{1}{4}\pi}}=\ln@{\sec@@{x}+\tan@@{x}}=\asinh@{\tan@@{x}}=\acsch@{\cot@@{x}}=\acosh@{\sec@@{x}}=\asech@{\cos@@{x}}=\atanh@{\sin@@{x}}=\acoth@{\csc@@{x}}.}
    0 references
    DLMF id
    DLMF:4.23.E42
    0 references
    Symbols used
    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.m2apdec
    0 references
    cosecant function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \csc@@{\NVar{z}}}
    xml-id
    C4.S14.E5.m2adec
    0 references
    cosine function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{\NVar{z}}}
    xml-id
    C4.S14.E2.m2aadec
    0 references
    cotangent function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cot@@{\NVar{z}}}
    xml-id
    C4.S14.E7.m2adec
    0 references
    inverse hyperbolic cosecant function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \acsch@@{\NVar{z}}}
    xml-id
    C4.S37.E7.m2adec
    0 references
    Q11246
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \acosh@@{\NVar{z}}}
    xml-id
    C4.S37.SS2.p1.m9adec
    0 references
    inverse hyperbolic cotangent function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \acoth@@{\NVar{z}}}
    xml-id
    C4.S37.E9.m2adec
    0 references
    inverse hyperbolic secant function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \asech@@{\NVar{z}}}
    xml-id
    C4.S37.E8.m2adec
    0 references
    Q11247
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \asinh@@{\NVar{z}}}
    xml-id
    C4.S37.SS2.p1.m8adec
    0 references
    Q11248
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \atanh@@{\NVar{z}}}
    xml-id
    C4.S37.SS2.p1.m10adec
    0 references
    inverse Gudermannian function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \aGudermannian@{\NVar{x}}}
    xml-id
    C4.S23.E41.m2aadec
    0 references
    principal branch of logarithm function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ln@@{\NVar{z}}}
    xml-id
    C4.S2.E2.m2aldec
    0 references
    secant function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sec@@{\NVar{z}}}
    xml-id
    C4.S14.E6.m2aadec
    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.m2aadec
    0 references
    tangent function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tan@@{\NVar{z}}}
    xml-id
    C4.S14.E4.m2aadec
    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.m1mdec
    0 references
     
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