DLMF:15.9.E15 (Q5105): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: gamma function / rank
 
Normal rank
Property / Symbols used: gamma function / qualifier
 
test:

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

Revision as of 13:10, 2 January 2020

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DLMF:15.9.E15
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    C α ( λ ) ( z ) = Γ ( α + 2 λ ) Γ ( 2 λ ) Γ ( α + 1 ) F ( - α , α + 2 λ λ + 1 2 ; 1 - z 2 ) . ultraspherical-Gegenbauer-polynomial 𝜆 𝛼 𝑧 Euler-Gamma 𝛼 2 𝜆 Euler-Gamma 2 𝜆 Euler-Gamma 𝛼 1 Gauss-hypergeometric-F 𝛼 𝛼 2 𝜆 𝜆 1 2 1 𝑧 2 {\displaystyle{\displaystyle C^{(\lambda)}_{\alpha}\left(z\right)=\frac{\Gamma% \left(\alpha+2\lambda\right)}{\Gamma\left(2\lambda\right)\Gamma\left(\alpha+1% \right)}F\left({-\alpha,\alpha+2\lambda\atop\lambda+\tfrac{1}{2}};\frac{1-z}{2% }\right).}}
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    Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    C5.S2.E1.m2aadec
    0 references