DLMF:33.16.E10 (Q9638): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q12666 / rank
 
Normal rank
Property / Symbols used: Q12666 / qualifier
 
Defining formula:

ℓ ℓ {\displaystyle{\displaystyle\ell}}

\ell
Property / Symbols used: Q12666 / qualifier
 
xml-id: C33.S1.XMD2.m1gdec

Revision as of 14:35, 2 January 2020

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DLMF:33.16.E10
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    Statements

    Defining formula
    f ⁡ ( ϵ , ℓ ; r ) = ( - 1 ) ℓ ⁢ ν ℓ + 1 ⁢ ( - cos ⁡ ( π ⁢ ν ) ⁢ ζ ℓ ⁢ ( ν , r ) Γ ⁡ ( ℓ + 1 + ν ) + sin ⁡ ( π ⁢ ν ) ⁢ Γ ⁡ ( ν - ℓ ) ⁢ ξ ℓ ⁢ ( ν , r ) π ) , Coulomb-f italic-ϵ ℓ 𝑟 superscript 1 ℓ superscript 𝜈 ℓ 1 𝜋 𝜈 subscript 𝜁 ℓ 𝜈 𝑟 Euler-Gamma ℓ 1 𝜈 𝜋 𝜈 Euler-Gamma 𝜈 ℓ subscript 𝜉 ℓ 𝜈 𝑟 𝜋 {\displaystyle{\displaystyle f\left(\epsilon,\ell;r\right)=(-1)^{\ell}\nu^{% \ell+1}\left(-\frac{\cos\left(\pi\nu\right)\zeta_{\ell}(\nu,r)}{\Gamma\left(% \ell+1+\nu\right)}+\frac{\sin\left(\pi\nu\right)\Gamma\left(\nu-\ell\right)\xi% _{\ell}(\nu,r)}{\pi}\right),}}
    0 references
    DLMF id
    DLMF:33.16.E10
    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.m2acdec
    0 references
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2adec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2afdec
    0 references
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2adec
    0 references
    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2adec
    0 references
    Q12666
    Defining formula
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C33.S1.XMD2.m1gdec
    0 references
     
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