DLMF:19.7.E10 (Q6205): Difference between revisions

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Property / Symbols defined
 
Property / Symbols defined: change of variable (locally) / rank
 
Normal rank
Property / constraint
 

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (k^{2}-\alpha^{2})(k^{2}-\omega^{2})=k^{2}(k^{2}-1)}

(k^{2}-\alpha^{2})(k^{2}-\omega^{2})=k^{2}(k^{2}-1)
Property / constraint: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (k^{2}-\alpha^{2})(k^{2}-\omega^{2})=k^{2}(k^{2}-1)} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Carlson’s combination of inverse circular and inverse hyperbolic functions / rank
 
Normal rank
Property / Symbols used: Carlson’s combination of inverse circular and inverse hyperbolic functions / qualifier
 
Defining formula:

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

\CarlsonellintRC@{\NVar{x}}{\NVar{y}}
Property / Symbols used: Carlson’s combination of inverse circular and inverse hyperbolic functions / qualifier
 
xml-id: C19.S2.E17.m2abdec
Property / Symbols used
 
Property / Symbols used: Legendre’s incomplete elliptic integral of the first kind / rank
 
Normal rank
Property / Symbols used: Legendre’s incomplete elliptic integral of the first kind / qualifier
 
Defining formula:

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

\incellintFk@{\NVar{\phi}}{\NVar{k}}
Property / Symbols used: Legendre’s incomplete elliptic integral of the first kind / qualifier
 
xml-id: C19.S2.E4.m2aedec
Property / Symbols used
 
Property / Symbols used: Legendre’s incomplete elliptic integral of the third kind / rank
 
Normal rank
Property / Symbols used: Legendre’s incomplete elliptic integral of the third kind / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintPik@{\NVar{\phi}}{\NVar{\alpha}^{2}}{\NVar{k}}}

\incellintPik@{\NVar{\phi}}{\NVar{\alpha}^{2}}{\NVar{k}}
Property / Symbols used: Legendre’s incomplete elliptic integral of the third kind / qualifier
 
xml-id: C19.S2.E7.m2aedec
Property / Symbols used
 
Property / Symbols used: Q11807 / rank
 
Normal rank
Property / Symbols used: Q11807 / qualifier
 
Defining formula:

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

\phi
Property / Symbols used: Q11807 / qualifier
 
xml-id: C19.S1.XMD4.m1fdec
Property / Symbols used
 
Property / Symbols used: Q11808 / rank
 
Normal rank
Property / Symbols used: Q11808 / qualifier
 
Defining formula:

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

k
Property / Symbols used: Q11808 / qualifier
 
xml-id: C19.S1.XMD5.m1idec
Property / Symbols used
 
Property / Symbols used: Q11809 / rank
 
Normal rank
Property / Symbols used: Q11809 / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha^{2}}

\alpha^{2}
Property / Symbols used: Q11809 / qualifier
 
xml-id: C19.S1.XMD7.m1fdec
Property / Symbols used
 
Property / Symbols used: Q11823 / rank
 
Normal rank
Property / Symbols used: Q11823 / qualifier
 
Defining formula:

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

c
Property / Symbols used: Q11823 / qualifier
 
xml-id: C19.S7.XMD9.m1bdec

Latest revision as of 13:42, 2 January 2020

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DLMF:19.7.E10
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    Statements

    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (1-\alpha^{2})\incellintPik@{\phi}{\alpha^{2}}{k}+(1-\omega^{2})\incellintPik@{\phi}{\omega^{2}}{k}=\incellintFk@{\phi}{k}+(1-\alpha^{2}-\omega^{2})\sqrt{c-k^{2}}\*\CarlsonellintRC@{c(c-1)}{(c-\alpha^{2})(c-\omega^{2})},}
    0 references
    DLMF id
    DLMF:19.7.E10
    0 references
    constraint
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (k^{2}-\alpha^{2})(k^{2}-\omega^{2})=k^{2}(k^{2}-1)}
    0 references
    Symbols used
    Carlson’s combination of inverse circular and inverse hyperbolic functions
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonellintRC@{\NVar{x}}{\NVar{y}}}
    xml-id
    C19.S2.E17.m2abdec
    0 references
    Legendre’s incomplete elliptic integral of the first kind
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintFk@{\NVar{\phi}}{\NVar{k}}}
    xml-id
    C19.S2.E4.m2aedec
    0 references
    Legendre’s incomplete elliptic integral of the third kind
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintPik@{\NVar{\phi}}{\NVar{\alpha}^{2}}{\NVar{k}}}
    xml-id
    C19.S2.E7.m2aedec
    0 references
    Q11807
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phi}
    xml-id
    C19.S1.XMD4.m1fdec
    0 references
    Q11808
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k}
    xml-id
    C19.S1.XMD5.m1idec
    0 references
    Q11809
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha^{2}}
    xml-id
    C19.S1.XMD7.m1fdec
    0 references
    Q11823
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c}
    xml-id
    C19.S7.XMD9.m1bdec
    0 references
     
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