DLMF:31.7.E1 (Q9024)

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DLMF:31.7.E1
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    Statements

    Defining formula
    F 1 2 ⁡ ( α , β ; γ ; z ) = H ⁢ ℓ ⁡ ( 1 , α ⁢ β ; α , β , γ , δ ; z ) = H ⁢ ℓ ⁡ ( 0 , 0 ; α , β , γ , α + β + 1 - γ ; z ) = H ⁢ ℓ ⁡ ( a , a ⁢ α ⁢ β ; α , β , γ , α + β + 1 - γ ; z ) . Gauss-hypergeometric-F-as-2F1 𝛼 𝛽 𝛾 𝑧 Heun-local 1 𝛼 𝛽 𝛼 𝛽 𝛾 𝛿 𝑧 Heun-local 0 0 𝛼 𝛽 𝛾 𝛼 𝛽 1 𝛾 𝑧 Heun-local 𝑎 𝑎 𝛼 𝛽 𝛼 𝛽 𝛾 𝛼 𝛽 1 𝛾 𝑧 {\displaystyle{\displaystyle{{}_{2}F_{1}}\left(\alpha,\beta;\gamma;z\right)=% \mathit{H\!\ell}\left(1,\alpha\beta;\alpha,\beta,\gamma,\delta;z\right)=% \mathit{H\!\ell}\left(0,0;\alpha,\beta,\gamma,\alpha+\beta+1-\gamma;z\right)=% \mathit{H\!\ell}\left(a,a\alpha\beta;\alpha,\beta,\gamma,\alpha+\beta+1-\gamma% ;z\right).}}
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    DLMF id
    DLMF:31.7.E1
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