DLMF:33.8.E2 (Q9543): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: irregular Coulomb radial functions / rank
 
Normal rank
Property / Symbols used: irregular Coulomb radial functions / qualifier
 
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)}}

\irregCoulombH{\NVar{\pm}}{\NVar{\ell}}@{\NVar{\eta}}{\NVar{\rho}}
Property / Symbols used: irregular Coulomb radial functions / qualifier
 
xml-id: C33.S2.E7.m2adec

Revision as of 14:26, 2 January 2020

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DLMF:33.8.E2
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    Statements

    Defining formula
    H ℓ ± ′ H ℓ ± = c ± i ρ ⁢ a ⁢ b 2 ⁢ ( ρ - η ± i ) + ( a + 1 ) ⁢ ( b + 1 ) 2 ⁢ ( ρ - η ± 2 ⁢ i ) + ⋯ , diffop irregular-Coulomb-H plus-or-minus ℓ 1 irregular-Coulomb-H plus-or-minus ℓ plus-or-minus 𝑐 imaginary-unit 𝜌 continued-fraction 𝑎 𝑏 2 plus-or-minus 𝜌 𝜂 imaginary-unit continued-fraction 𝑎 1 𝑏 1 2 plus-or-minus 𝜌 𝜂 2 imaginary-unit ⋯ {\displaystyle{\displaystyle\frac{{H^{\pm}_{\ell}}'}{{H^{\pm}_{\ell}}}=c\pm% \frac{\mathrm{i}}{\rho}\cfrac{ab}{2(\rho-\eta\pm\mathrm{i})+\cfrac{(a+1)(b+1)}% {2(\rho-\eta\pm 2\mathrm{i})+\cdots}},}}
    0 references
    DLMF id
    DLMF:33.8.E2
    0 references
    Symbols used
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    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.m2adec
    0 references
     
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