DLMF:15.9.E15 (Q5105)

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DLMF:15.9.E15
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    Statements

    test
    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).}}
    0 references
    DLMF id
    DLMF:15.9.E15
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aadec
    0 references
     
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