DLMF:33.14.E12 (Q9622): Difference between revisions

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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.m2aadec
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.m1hdec
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.m1kdec
Property / Symbols used
 
Property / Symbols used: quantity (locally) / rank
 
Normal rank
Property / Symbols used: quantity (locally) / qualifier
 
Defining formula:

κ 𝜅 {\displaystyle{\displaystyle\kappa}}

\kappa
Property / Symbols used: quantity (locally) / qualifier
 
xml-id: C33.S14.XMD1.m1ddec
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.m1bdec

Latest revision as of 14:32, 2 January 2020

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DLMF:33.14.E12
No description defined

    Statements

    Defining formula
    A ⁢ ( ϵ , ℓ ) = Γ ⁡ ( 1 + ℓ + κ ) Γ ⁡ ( κ - ℓ ) ⁢ κ - 2 ⁢ ℓ - 1 , 𝐴 italic-ϵ ℓ Euler-Gamma 1 ℓ 𝜅 Euler-Gamma 𝜅 ℓ superscript 𝜅 2 ℓ 1 {\displaystyle{\displaystyle A(\epsilon,\ell)=\frac{\Gamma\left(1+\ell+\kappa% \right)}{\Gamma\left(\kappa-\ell\right)}\kappa^{-2\ell-1},}}
    0 references
    DLMF id
    DLMF:33.14.E12
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aadec
    0 references
    Q12666
    Defining formula
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C33.S1.XMD2.m1hdec
    0 references
    Q12693
    Defining formula
    ϵ italic-ϵ {\displaystyle{\displaystyle\epsilon}}
    xml-id
    C33.S1.XMD6.m1kdec
    0 references
    quantity (locally)
    Defining formula
    κ 𝜅 {\displaystyle{\displaystyle\kappa}}
    xml-id
    C33.S14.XMD1.m1ddec
    0 references
    function (locally)
    Defining formula
    A ⁢ ( ϵ , ℓ ) 𝐴 italic-ϵ ℓ {\displaystyle{\displaystyle A(\epsilon,\ell)}}
    xml-id
    C33.S14.XMD4.m1bdec
    0 references
     
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