DLMF:33.16.E12 (Q9640): Difference between revisions

From DRMF
Jump to navigation Jump to search
‎Created a new Item: Wikidata Toolkit example test item creation
 
‎Changed an Item: Add constraint
 
(10 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: regular Coulomb function / rank
 
Normal rank
Property / Symbols used: regular Coulomb function / qualifier
 
Defining formula:

f ⁡ ( ϵ , ℓ ; r ) Coulomb-f italic-ϵ ℓ 𝑟 {\displaystyle{\displaystyle f\left(\NVar{\epsilon},\NVar{\ell};\NVar{r}\right% )}}

\regCoulombf@{\NVar{\epsilon}}{\NVar{\ell}}{\NVar{r}}
Property / Symbols used: regular Coulomb function / qualifier
 
xml-id: C33.S14.E4.m2addec
Property / Symbols used
 
Property / Symbols used: gamma function / rank
 
Normal rank
Property / Symbols used: gamma function / qualifier
 
Defining formula:

Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

\EulerGamma@{\NVar{z}}
Property / Symbols used: gamma function / qualifier
 
xml-id: C5.S2.E1.m2abdec
Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
Defining formula:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2ahdec
Property / Symbols used
 
Property / Symbols used: cosine function / rank
 
Normal rank
Property / Symbols used: cosine function / qualifier
 
Defining formula:

cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}

\cos@@{\NVar{z}}
Property / Symbols used: cosine function / qualifier
 
xml-id: C4.S14.E2.m2abdec
Property / Symbols used
 
Property / Symbols used: sine function / rank
 
Normal rank
Property / Symbols used: sine function / qualifier
 
Defining formula:

sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}

\sin@@{\NVar{z}}
Property / Symbols used: sine function / qualifier
 
xml-id: C4.S14.E1.m2abdec
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.m1idec
Property / Symbols used
 
Property / Symbols used: Q12692 / rank
 
Normal rank
Property / Symbols used: Q12692 / qualifier
 
Defining formula:

r 𝑟 {\displaystyle{\displaystyle r}}

r
Property / Symbols used: Q12692 / qualifier
 
xml-id: C33.S1.XMD3.m1gdec
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.m1hdec
Property / Symbols used
 
Property / Symbols used: parameter (locally) / rank
 
Normal rank
Property / Symbols used: parameter (locally) / qualifier
 
Defining formula:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: parameter (locally) / qualifier
 
xml-id: C33.S16.XMD2.m1ddec
Property / Symbols used
 
Property / Symbols used: Q12694 / rank
 
Normal rank
Property / Symbols used: Q12694 / qualifier
 
Defining formula:

ζ ℓ ⁢ ( ν , r ) subscript 𝜁 ℓ 𝜈 𝑟 {\displaystyle{\displaystyle\zeta_{\ell}(\nu,r)}}

\zeta_{\ell}(\nu,r)
Property / Symbols used: Q12694 / qualifier
 
xml-id: C33.S16.XMD3.m1cdec
Property / Symbols used
 
Property / Symbols used: Q12695 / rank
 
Normal rank
Property / Symbols used: Q12695 / qualifier
 
Defining formula:

ξ ℓ ⁢ ( ν , r ) subscript 𝜉 ℓ 𝜈 𝑟 {\displaystyle{\displaystyle\xi_{\ell}(\nu,r)}}

\xi_{\ell}(\nu,r)
Property / Symbols used: Q12695 / qualifier
 
xml-id: C33.S16.XMD4.m1cdec

Latest revision as of 14:36, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:33.16.E12
No description defined

    Statements

    Defining formula
    f ⁡ ( ϵ , ℓ ; r ) = ( - 1 ) ℓ ⁢ ν ℓ + 1 π ⁢ ( - π ⁢ ξ ℓ ⁢ ( - ν , r ) Γ ⁡ ( ℓ + 1 + ν ) + sin ⁡ ( π ⁢ ν ) ⁢ cos ⁡ ( π ⁢ ν ) ⁢ Γ ⁡ ( ν - ℓ ) ⁢ ζ ℓ ⁢ ( - ν , r ) ) , Coulomb-f italic-ϵ ℓ 𝑟 superscript 1 ℓ superscript 𝜈 ℓ 1 𝜋 𝜋 subscript 𝜉 ℓ 𝜈 𝑟 Euler-Gamma ℓ 1 𝜈 𝜋 𝜈 𝜋 𝜈 Euler-Gamma 𝜈 ℓ subscript 𝜁 ℓ 𝜈 𝑟 {\displaystyle{\displaystyle f\left(\epsilon,\ell;r\right)=\frac{(-1)^{\ell}% \nu^{\ell+1}}{\pi}\left(-\frac{\pi\xi_{\ell}(-\nu,r)}{\Gamma\left(\ell+1+\nu% \right)}+\sin\left(\pi\nu\right)\cos\left(\pi\nu\right)\Gamma\left(\nu-\ell% \right)\zeta_{\ell}(-\nu,r)\right),}}
    0 references
    DLMF id
    DLMF:33.16.E12
    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.m2addec
    0 references
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2abdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2ahdec
    0 references
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2abdec
    0 references
    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2abdec
    0 references
    Q12666
    Defining formula
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C33.S1.XMD2.m1idec
    0 references
    Q12692
    Defining formula
    r 𝑟 {\displaystyle{\displaystyle r}}
    xml-id
    C33.S1.XMD3.m1gdec
    0 references
    Q12693
    Defining formula
    ϵ italic-ϵ {\displaystyle{\displaystyle\epsilon}}
    xml-id
    C33.S1.XMD6.m1hdec
    0 references
    parameter (locally)
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C33.S16.XMD2.m1ddec
    0 references
    Q12694
    Defining formula
    ζ ℓ ⁢ ( ν , r ) subscript 𝜁 ℓ 𝜈 𝑟 {\displaystyle{\displaystyle\zeta_{\ell}(\nu,r)}}
    xml-id
    C33.S16.XMD3.m1cdec
    0 references
    Q12695
    Defining formula
    ξ ℓ ⁢ ( ν , r ) subscript 𝜉 ℓ 𝜈 𝑟 {\displaystyle{\displaystyle\xi_{\ell}(\nu,r)}}
    xml-id
    C33.S16.XMD4.m1cdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q9640&oldid=48878"