DLMF:33.16.E4 (Q9631): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12666 / rank
 
Normal rank
Property / Symbols used: Q12666 / qualifier
 
Defining formula:

ℓ ℓ {\displaystyle{\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:

r 𝑟 {\displaystyle{\displaystyle r}}

r
Property / Symbols used: Q12692 / qualifier
 
xml-id: C33.S1.XMD3.m1dec
Property / Symbols used
 
Property / Symbols used: Q12693 / rank
 
Normal rank
Property / Symbols used: Q12693 / qualifier
 
Defining formula:

ϵ italic-ϵ {\displaystyle{\displaystyle\epsilon}}

\epsilon
Property / Symbols used: Q12693 / qualifier
 
xml-id: C33.S1.XMD6.m1adec
Property / Symbols used
 
Property / Symbols used: function (locally) / rank
 
Normal rank
Property / Symbols used: function (locally) / qualifier
 
Defining formula:

A ⁢ ( ϵ , ℓ ) 𝐴 italic-ϵ ℓ {\displaystyle{\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: parameter (locally) / rank
 
Normal rank
Property / Symbols used: parameter (locally) / qualifier
 
Defining formula:

τ 𝜏 {\displaystyle{\displaystyle\tau}}

\tau
Property / Symbols used: parameter (locally) / qualifier
 
xml-id: C33.S16.XMD1.m1adec

Latest revision as of 14:34, 2 January 2020

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DLMF:33.16.E4
No description defined

    Statements

    Defining formula
    f ⁡ ( ϵ , ℓ ; r ) = ( 2 π ⁢ τ ⁢ 1 - e - 2 ⁢ π / τ A ⁢ ( ϵ , ℓ ) ) 1 / 2 ⁢ F ℓ ⁡ ( - 1 / τ , τ ⁢ r ) , Coulomb-f italic-ϵ ℓ 𝑟 superscript 2 𝜋 𝜏 1 superscript 𝑒 2 𝜋 𝜏 𝐴 italic-ϵ ℓ 1 2 regular-Coulomb-F ℓ 1 𝜏 𝜏 𝑟 {\displaystyle{\displaystyle f\left(\epsilon,\ell;r\right)=\left(\frac{2}{\pi% \tau}\frac{1-e^{-2\pi/\tau}}{A(\epsilon,\ell)}\right)^{\ifrac{1}{2}}F_{\ell}% \left(-1/\tau,\tau r\right),}}
    0 references
    DLMF id
    DLMF:33.16.E4
    0 references
    Symbols used
    regular Coulomb function
    Defining formula
    f ⁡ ( ϵ , ℓ ; r ) Coulomb-f italic-ϵ ℓ 𝑟 {\displaystyle{\displaystyle f\left(\NVar{\epsilon},\NVar{\ell};\NVar{r}\right% )}}
    xml-id
    C33.S14.E4.m2aadec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    regular Coulomb radial function
    Defining formula
    F ℓ ⁡ ( η , ρ ) regular-Coulomb-F ℓ 𝜂 𝜌 {\displaystyle{\displaystyle F_{\NVar{\ell}}\left(\NVar{\eta},\NVar{\rho}% \right)}}
    xml-id
    C33.S2.E3.m2aadec
    0 references
    Q12666
    Defining formula
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C33.S1.XMD2.m1bdec
    0 references
    Q12692
    Defining formula
    r 𝑟 {\displaystyle{\displaystyle r}}
    xml-id
    C33.S1.XMD3.m1dec
    0 references
    Q12693
    Defining formula
    ϵ italic-ϵ {\displaystyle{\displaystyle\epsilon}}
    xml-id
    C33.S1.XMD6.m1adec
    0 references
    function (locally)
    Defining formula
    A ⁢ ( ϵ , ℓ ) 𝐴 italic-ϵ ℓ {\displaystyle{\displaystyle A(\epsilon,\ell)}}
    xml-id
    C33.S14.XMD4.m1dec
    0 references
    parameter (locally)
    Defining formula
    τ 𝜏 {\displaystyle{\displaystyle\tau}}
    xml-id
    C33.S16.XMD1.m1adec
    0 references
     
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