DLMF:33.16.E1 (Q9628): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older edit
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
Property / Symbols used
 
Property / Symbols used: Q12668 / rank
 
Normal rank
Property / Symbols used: Q12668 / qualifier
 
Defining formula:

η 𝜂 {\displaystyle{\displaystyle\eta}}

\eta
Property / Symbols used: Q12668 / qualifier
 
xml-id: C33.S1.XMD7.m1dec

Latest revision as of 14:33, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:33.16.E1
No description defined

    Statements

    Defining formula
    F ℓ ⁡ ( η , ρ ) = ( 2 ⁢ ℓ + 1 ) ! ⁢ C ℓ ⁡ ( η ) ( - 2 ⁢ η ) ℓ + 1 ⁢ f ⁡ ( 1 / η 2 , ℓ ; - η ⁢ ρ ) , regular-Coulomb-F ℓ 𝜂 𝜌 2 ℓ 1 Coulomb-C ℓ 𝜂 superscript 2 𝜂 ℓ 1 Coulomb-f 1 superscript 𝜂 2 ℓ 𝜂 𝜌 {\displaystyle{\displaystyle F_{\ell}\left(\eta,\rho\right)=\dfrac{(2\ell+1)!C% _{\ell}\left(\eta\right)}{(-2\eta)^{\ell+1}}f\left(1/\eta^{2},\ell;-\eta\rho% \right),}}
    0 references
    DLMF id
    DLMF:33.16.E1
    0 references
    Symbols used
    normalizing constant for Coulomb radial functions
    Defining formula
    C ℓ ⁡ ( η ) Coulomb-C ℓ 𝜂 {\displaystyle{\displaystyle C_{\NVar{\ell}}\left(\NVar{\eta}\right)}}
    xml-id
    C33.S2.E5.m2adec
    0 references
    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.m2adec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
    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.m2adec
    0 references
    Q12666
    Defining formula
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C33.S1.XMD2.m1dec
    0 references
    Q12667
    Defining formula
    ρ 𝜌 {\displaystyle{\displaystyle\rho}}
    xml-id
    C33.S1.XMD5.m1dec
    0 references
    Q12668
    Defining formula
    η 𝜂 {\displaystyle{\displaystyle\eta}}
    xml-id
    C33.S1.XMD7.m1dec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q9628&oldid=48399"