DLMF:29.5.E5 (Q8623): Difference between revisions

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‎Changed an Item: Add constraint
 
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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 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: Q12357 / rank
 
Normal rank
Property / Symbols used: Q12357 / qualifier
 
Defining formula:

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

m
Property / Symbols used: Q12357 / qualifier
 
xml-id: C29.S1.XMD1.m1cdec
Property / Symbols used
 
Property / Symbols used: Q12348 / rank
 
Normal rank
Property / Symbols used: Q12348 / qualifier
 
Defining formula:

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

z
Property / Symbols used: Q12348 / qualifier
 
xml-id: C29.S1.XMD6.m1bdec
Property / Symbols used
 
Property / Symbols used: Q12350 / rank
 
Normal rank
Property / Symbols used: Q12350 / qualifier
 
Defining formula:

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

k
Property / Symbols used: Q12350 / qualifier
 
xml-id: C29.S1.XMD8.m1adec
Property / Symbols used
 
Property / Symbols used: Q12351 / rank
 
Normal rank
Property / Symbols used: Q12351 / qualifier
 
Defining formula:

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

\nu
Property / Symbols used: Q12351 / qualifier
 
xml-id: C29.S1.XMD9.m1ddec
Property / Symbols used
 
Property / Symbols used: Q12363 / rank
 
Normal rank
Property / Symbols used: Q12363 / qualifier
 
Defining formula:

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

\mu
Property / Symbols used: Q12363 / qualifier
 
xml-id: C29.S5.XMD1.m1adec

Latest revision as of 14:46, 2 January 2020

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DLMF:29.5.E5
No description defined

    Statements

    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\lim_{k\to 1-}\frac{\LameEc{m}{\nu}@{z}{k^{2}}}{\LameEc{m}{\nu}@{0}{k^{2}}}=\lim_{k\to 1-}\frac{\LameEs{m+1}{\nu}@{z}{k^{2}}}{\LameEs{m+1}{\nu}@{0}{k^{2}}}}=\frac{1}{(\cosh@@{z})^{\mu}}\hyperF@@{\tfrac{1}{2}\mu-\tfrac{1}{2}\nu}{\tfrac{1}{2}\mu+\tfrac{1}{2}\nu+\tfrac{1}{2}}{\tfrac{1}{2}}{\tanh^{2}@@{z}},}
    0 references
    DLMF id
    DLMF:29.5.E5
    0 references
    constraint
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle m}
    0 references
    Symbols used
    $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@{\NVar{a}}{\NVar{b}}{\NVar{c}}{\NVar{z}}}
    xml-id
    C15.S2.E1.m2adec
    0 references
    Q12362
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LameEc{\NVar{m}}{\NVar{\nu}}@{\NVar{z}}{\NVar{k^{2}}}}
    xml-id
    C29.S3.SS4.p1.m5abdec
    0 references
    Q12364
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LameEs{\NVar{m}}{\NVar{\nu}}@{\NVar{z}}{\NVar{k^{2}}}}
    xml-id
    C29.S3.SS4.p1.m6aadec
    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 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
    Q12357
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle m}
    xml-id
    C29.S1.XMD1.m1cdec
    0 references
    Q12348
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z}
    xml-id
    C29.S1.XMD6.m1bdec
    0 references
    Q12350
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k}
    xml-id
    C29.S1.XMD8.m1adec
    0 references
    Q12351
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \nu}
    xml-id
    C29.S1.XMD9.m1ddec
    0 references
    Q12363
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mu}
    xml-id
    C29.S5.XMD1.m1adec
    0 references
     
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