DLMF:33.16.E12 (Q9640): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
Defining formula:

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

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2ahdec
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.m2abdec
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.m2abdec
Property / Symbols used
 
Property / Symbols used: Q12666 / rank
 
Normal rank
Property / Symbols used: Q12666 / qualifier
 
Defining formula:

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

\ell
Property / Symbols used: Q12666 / qualifier
 
xml-id: C33.S1.XMD2.m1idec
Property / Symbols used
 
Property / Symbols used: Q12692 / rank
 
Normal rank
Property / Symbols used: Q12692 / qualifier
 
Defining formula:

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

r
Property / Symbols used: Q12692 / qualifier
 
xml-id: C33.S1.XMD3.m1gdec
Property / Symbols used
 
Property / Symbols used: Q12693 / rank
 
Normal rank
Property / Symbols used: Q12693 / qualifier
 
Defining formula:

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

\epsilon
Property / Symbols used: Q12693 / qualifier
 
xml-id: C33.S1.XMD6.m1hdec
Property / Symbols used
 
Property / Symbols used: parameter (locally) / rank
 
Normal rank
Property / Symbols used: parameter (locally) / qualifier
 
Defining formula:

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

\nu
Property / Symbols used: parameter (locally) / qualifier
 
xml-id: C33.S16.XMD2.m1ddec
Property / Symbols used
 
Property / Symbols used: Q12694 / rank
 
Normal rank
Property / Symbols used: Q12694 / qualifier
 
Defining formula:

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

\zeta_{\ell}(\nu,r)
Property / Symbols used: Q12694 / qualifier
 
xml-id: C33.S16.XMD3.m1cdec
Property / Symbols used
 
Property / Symbols used: Q12695 / rank
 
Normal rank
Property / Symbols used: Q12695 / qualifier
 
Defining formula:

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

\xi_{\ell}(\nu,r)
Property / Symbols used: Q12695 / qualifier
 
xml-id: C33.S16.XMD4.m1cdec

Latest revision as of 14:36, 2 January 2020

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DLMF:33.16.E12
No description defined

    Statements

    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \regCoulombf@{\epsilon}{\ell}{r}=\frac{(-1)^{\ell}\nu^{\ell+1}}{\pi}\left(-\frac{\pi\xi_{\ell}(-\nu,r)}{\EulerGamma@{\ell+1+\nu}}+\sin@{\pi\nu}\cos@{\pi\nu}\EulerGamma@{\nu-\ell}\zeta_{\ell}(-\nu,r)\right),}
    0 references
    DLMF id
    DLMF:33.16.E12
    0 references
    Symbols used
    regular Coulomb function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \regCoulombf@{\NVar{\epsilon}}{\NVar{\ell}}{\NVar{r}}}
    xml-id
    C33.S14.E4.m2addec
    0 references
    gamma function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulerGamma@{\NVar{z}}}
    xml-id
    C5.S2.E1.m2abdec
    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.m2ahdec
    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.m2abdec
    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.m2abdec
    0 references
    Q12666
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ell}
    xml-id
    C33.S1.XMD2.m1idec
    0 references
    Q12692
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle r}
    xml-id
    C33.S1.XMD3.m1gdec
    0 references
    Q12693
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \epsilon}
    xml-id
    C33.S1.XMD6.m1hdec
    0 references
    parameter (locally)
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \nu}
    xml-id
    C33.S16.XMD2.m1ddec
    0 references
    Q12694
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \zeta_{\ell}(\nu,r)}
    xml-id
    C33.S16.XMD3.m1cdec
    0 references
    Q12695
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \xi_{\ell}(\nu,r)}
    xml-id
    C33.S16.XMD4.m1cdec
    0 references
     
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