DLMF:33.19.E3 (Q9661): Difference between revisions

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‎Changed an Item: Add constraint
 
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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.m2adec
Property / Symbols used
 
Property / Symbols used: Q10811 / rank
 
Normal rank
Property / Symbols used: Q10811 / qualifier
 
Defining formula:

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

\realpart@@
Property / Symbols used: Q10811 / qualifier
 
xml-id: C1.S9.E2.m1adec
Property / Symbols used
 
Property / Symbols used: Q12669 / rank
 
Normal rank
Property / Symbols used: Q12669 / qualifier
 
Defining formula:

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

k
Property / Symbols used: Q12669 / qualifier
 
xml-id: C33.S1.XMD1.m1bdec
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.m1bdec
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.m1adec
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.m1bdec
Property / Symbols used
 
Property / Symbols used: quantity (locally) / rank
 
Normal rank
Property / Symbols used: quantity (locally) / qualifier
 
Defining formula:

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

\kappa
Property / Symbols used: quantity (locally) / qualifier
 
xml-id: C33.S14.XMD1.m1dec
Property / Symbols used
 
Property / Symbols used: function (locally) / rank
 
Normal rank
Property / Symbols used: function (locally) / qualifier
 
Defining formula:

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

A(\epsilon,\ell)
Property / Symbols used: function (locally) / qualifier
 
xml-id: C33.S14.XMD4.m1dec
Property / Symbols used
 
Property / Symbols used: Q12697 / rank
 
Normal rank
Property / Symbols used: Q12697 / qualifier
 
Defining formula:

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

\gamma_{k}
Property / Symbols used: Q12697 / qualifier
 
xml-id: C33.S19.XMD2.m1dec
Property / Symbols used
 
Property / Symbols used: Q12698 / rank
 
Normal rank
Property / Symbols used: Q12698 / qualifier
 
Defining formula:

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

\delta_{k}
Property / Symbols used: Q12698 / qualifier
 
xml-id: C33.S19.XMD3.m1dec

Latest revision as of 13:37, 2 January 2020

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English
DLMF:33.19.E3
No description defined

    Statements

    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\pi\irregCoulombh@{\epsilon}{\ell}{r}={\sum_{k=0}^{2\ell}\frac{(2\ell-k)!\gamma_{k}}{k!}(2r)^{k-\ell}-\sum_{k=0}^{\infty}\delta_{k}r^{k+\ell+1}}-A(\epsilon,\ell)\left(2\ln@@{|2r/\kappa|}+\realpart@@{\digamma@{\ell+1+\kappa}}+\realpart@@{\digamma@{-\ell+\kappa}}\right){\regCoulombf@{\epsilon}{\ell}{r},}}
    0 references
    DLMF id
    DLMF:33.19.E3
    0 references
    constraint
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle r\neq 0}
    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.m2aadec
    0 references
    irregular Coulomb function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \irregCoulombh@{\NVar{\epsilon}}{\NVar{\ell}}{\NVar{r}}}
    xml-id
    C33.S14.E7.m2adec
    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.m2adec
    0 references
    psi (or digamma) function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \digamma@{\NVar{z}}}
    xml-id
    C5.S2.E2.m2adec
    0 references
    Q10755
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle !}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
    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.m2adec
    0 references
    Q10811
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@}
    xml-id
    C1.S9.E2.m1adec
    0 references
    Q12669
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k}
    xml-id
    C33.S1.XMD1.m1bdec
    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.m1bdec
    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.m1adec
    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.m1bdec
    0 references
    quantity (locally)
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \kappa}
    xml-id
    C33.S14.XMD1.m1dec
    0 references
    function (locally)
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A(\epsilon,\ell)}
    xml-id
    C33.S14.XMD4.m1dec
    0 references
    Q12697
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma_{k}}
    xml-id
    C33.S19.XMD2.m1dec
    0 references
    Q12698
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \delta_{k}}
    xml-id
    C33.S19.XMD3.m1dec
    0 references
     
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