DLMF:31.7.E2 (Q9025)

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DLMF:31.7.E2
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    Statements

    Defining formula
    H ⁢ ℓ ⁡ ( 2 , α ⁢ β ; α , β , γ , α + β - 2 ⁢ γ + 1 ; z ) = F 1 2 ⁡ ( 1 2 ⁢ α , 1 2 ⁢ β ; γ ; 1 - ( 1 - z ) 2 ) , Heun-local 2 𝛼 𝛽 𝛼 𝛽 𝛾 𝛼 𝛽 2 𝛾 1 𝑧 Gauss-hypergeometric-F-as-2F1 1 2 𝛼 1 2 𝛽 𝛾 1 superscript 1 𝑧 2 {\displaystyle{\displaystyle\mathit{H\!\ell}\left(2,\alpha\beta;\alpha,\beta,% \gamma,\alpha+\beta-2\gamma+1;z\right)={{}_{2}F_{1}}\left(\tfrac{1}{2}\alpha,% \tfrac{1}{2}\beta;\gamma;1-(1-z)^{2}\right),}}
    0 references
    DLMF id
    DLMF:31.7.E2
    0 references
    Symbols used
    Q11581
    Defining formula
    F 1 2 ⁡ ( a , b ; c ; z ) Gauss-hypergeometric-F-as-2F1 𝑎 𝑏 𝑐 𝑧 {\displaystyle{\displaystyle{{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};% \NVar{z}\right)}}
    xml-id
    C16.S2.m5aadec
    0 references
     
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