DLMF:33.11.E4 (Q9582): Difference between revisions

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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.m1cdec
Property / Symbols used
 
Property / Symbols used: Q12683 / rank
 
Normal rank
Property / Symbols used: Q12683 / qualifier
 
Defining formula:

f ⁢ ( η , ρ ) 𝑓 𝜂 𝜌 {\displaystyle{\displaystyle f(\eta,\rho)}}

f(\eta,\rho)
Property / Symbols used: Q12683 / qualifier
 
xml-id: C33.S11.XMD1.m1bdec
Property / Symbols used
 
Property / Symbols used: Q12684 / rank
 
Normal rank
Property / Symbols used: Q12684 / qualifier
 
Defining formula:

g ⁢ ( η , ρ ) 𝑔 𝜂 𝜌 {\displaystyle{\displaystyle g(\eta,\rho)}}

g(\eta,\rho)
Property / Symbols used: Q12684 / qualifier
 
xml-id: C33.S11.XMD2.m1bdec

Latest revision as of 14:29, 2 January 2020

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DLMF:33.11.E4
No description defined

    Statements

    Defining formula
    H ℓ ± ⁡ ( η , ρ ) = e ± i ⁢ θ ℓ ⁢ ( f ⁢ ( η , ρ ) ± i ⁢ g ⁢ ( η , ρ ) ) , irregular-Coulomb-H plus-or-minus ℓ 𝜂 𝜌 superscript 𝑒 plus-or-minus imaginary-unit Coulomb-phase ℓ plus-or-minus 𝑓 𝜂 𝜌 imaginary-unit 𝑔 𝜂 𝜌 {\displaystyle{\displaystyle{H^{\pm}_{\ell}}\left(\eta,\rho\right)=e^{\pm% \mathrm{i}{\theta_{\ell}}}(f(\eta,\rho)\pm\mathrm{i}g(\eta,\rho)),}}
    0 references
    DLMF id
    DLMF:33.11.E4
    0 references
    Symbols used
    phase of Coulomb functions
    Defining formula
    θ ℓ ⁡ ( η , ρ ) Coulomb-phase ℓ 𝜂 𝜌 {\displaystyle{\displaystyle{\theta_{\NVar{\ell}}}\left(\NVar{\eta},\NVar{\rho% }\right)}}
    xml-id
    C33.S2.E9.m2acdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
    0 references
    irregular Coulomb radial functions
    Defining formula
    H ℓ ± ⁡ ( η , ρ ) irregular-Coulomb-H plus-or-minus ℓ 𝜂 𝜌 {\displaystyle{\displaystyle{H^{\NVar{\pm}}_{\NVar{\ell}}}\left(\NVar{\eta},% \NVar{\rho}\right)}}
    xml-id
    C33.S2.E7.m2aadec
    0 references
    Q12666
    Defining formula
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C33.S1.XMD2.m1cdec
    0 references
    Q12667
    Defining formula
    ρ 𝜌 {\displaystyle{\displaystyle\rho}}
    xml-id
    C33.S1.XMD5.m1cdec
    0 references
    Q12668
    Defining formula
    η 𝜂 {\displaystyle{\displaystyle\eta}}
    xml-id
    C33.S1.XMD7.m1cdec
    0 references
    Q12683
    Defining formula
    f ⁢ ( η , ρ ) 𝑓 𝜂 𝜌 {\displaystyle{\displaystyle f(\eta,\rho)}}
    xml-id
    C33.S11.XMD1.m1bdec
    0 references
    Q12684
    Defining formula
    g ⁢ ( η , ρ ) 𝑔 𝜂 𝜌 {\displaystyle{\displaystyle g(\eta,\rho)}}
    xml-id
    C33.S11.XMD2.m1bdec
    0 references
     
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