DLMF:33.20.E7 (Q9676): Difference between revisions

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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: Q12702 / rank
 
Normal rank
Property / Symbols used: Q12702 / qualifier
 
Defining formula:

𝖧 k ⁢ ( ℓ ; r ) subscript 𝖧 𝑘 ℓ 𝑟 {\displaystyle{\displaystyle\mathsf{H}_{k}(\ell;r)}}

\mathsf{H}_{k}(\ell;r)
Property / Symbols used: Q12702 / qualifier
 
xml-id: C33.S20.XMD3.m1dec

Latest revision as of 14:39, 2 January 2020

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DLMF:33.20.E7
No description defined

    Statements

    Defining formula
    h ⁡ ( ϵ , ℓ ; r ) ∼ - A ⁢ ( ϵ , ℓ ) ⁢ ∑ k = 0 ∞ ϵ k ⁢ 𝖧 k ⁢ ( ℓ ; r ) , asymptotic-expansion Coulomb-h italic-ϵ ℓ 𝑟 𝐴 italic-ϵ ℓ superscript subscript 𝑘 0 superscript italic-ϵ 𝑘 subscript 𝖧 𝑘 ℓ 𝑟 {\displaystyle{\displaystyle h\left(\epsilon,\ell;r\right)\sim-A(\epsilon,\ell% )\sum_{k=0}^{\infty}\epsilon^{k}{\sf H}_{k}(\ell;r),}}
    0 references
    DLMF id
    DLMF:33.20.E7
    0 references
    Symbols used
    irregular Coulomb function
    Defining formula
    h ⁡ ( ϵ , ℓ ; r ) Coulomb-h italic-ϵ ℓ 𝑟 {\displaystyle{\displaystyle h\left(\NVar{\epsilon},\NVar{\ell};\NVar{r}\right% )}}
    xml-id
    C33.S14.E7.m2abdec
    0 references
    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11adec
    0 references
    Q12669
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C33.S1.XMD1.m1ddec
    0 references
    Q12666
    Defining formula
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C33.S1.XMD2.m1fdec
    0 references
    Q12692
    Defining formula
    r 𝑟 {\displaystyle{\displaystyle r}}
    xml-id
    C33.S1.XMD3.m1edec
    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
    Q12702
    Defining formula
    𝖧 k ⁢ ( ℓ ; r ) subscript 𝖧 𝑘 ℓ 𝑟 {\displaystyle{\displaystyle\mathsf{H}_{k}(\ell;r)}}
    xml-id
    C33.S20.XMD3.m1dec
    0 references
     
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