DLMF:31.7.E1 (Q9024)

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DLMF:31.7.E1
No description defined

    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).}}
    0 references
    DLMF id
    DLMF:31.7.E1
    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.m5adec
    0 references
    Heun functions
    Defining formula
    H ⁢ ℓ ⁡ ( a , q ; α , β , γ , missing ; missing ) Heun-local 𝑎 𝑞 𝛼 𝛽 𝛾 missing missing {\displaystyle{\displaystyle\mathit{H\!\ell}\left(\NVar{a},\NVar{q};\NVar{% \alpha},\NVar{\beta},\NVar{\gamma},\NVar{missing};missing\right)\)\@add@PDF@RDFa@triples\end{document}}}
    xml-id
    C31.S3.E1.m2adec
    0 references
    Q12457
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C31.S1.XMD1.m1dec
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    Q12458
    Defining formula
    γ 𝛾 {\displaystyle{\displaystyle\gamma}}
    xml-id
    C31.S1.XMD10.m1dec
    0 references
    Q12459
    Defining formula
    δ 𝛿 {\displaystyle{\displaystyle\delta}}
    xml-id
    C31.S1.XMD11.m1dec
    0 references
    Q12461
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C31.S1.XMD6.m1dec
    0 references
    Q12463
    Defining formula
    α 𝛼 {\displaystyle{\displaystyle\alpha}}
    xml-id
    C31.S1.XMD8.m1dec
    0 references
    Q12464
    Defining formula
    β 𝛽 {\displaystyle{\displaystyle\beta}}
    xml-id
    C31.S1.XMD9.m1dec
    0 references
     
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