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

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
Defining formula:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2adec

Revision as of 14:34, 2 January 2020

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DLMF:33.16.E4
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    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
     
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