DLMF:31.3.E9 (Q9013)

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DLMF:31.3.E9
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    Statements

    Defining formula
    ( a - z a - 1 ) 1 - ϵ ⁢ H ⁢ ℓ ⁡ ( a a - 1 , ( a ⁢ ( δ + γ ) - γ ) ⁢ ( 1 - ϵ ) a - 1 + α ⁢ β ⁢ a - q a - 1 ; α + 1 - ϵ , β + 1 - ϵ , 2 - ϵ , δ ; a - z a - 1 ) . superscript 𝑎 𝑧 𝑎 1 1 italic-ϵ Heun-local 𝑎 𝑎 1 𝑎 𝛿 𝛾 𝛾 1 italic-ϵ 𝑎 1 𝛼 𝛽 𝑎 𝑞 𝑎 1 𝛼 1 italic-ϵ 𝛽 1 italic-ϵ 2 italic-ϵ 𝛿 𝑎 𝑧 𝑎 1 {\displaystyle{\displaystyle\left(\frac{a-z}{a-1}\right)^{1-\epsilon}\mathit{H% \!\ell}\left(\frac{a}{a-1},\frac{(a(\delta+\gamma)-\gamma)(1-\epsilon)}{a-1}+% \frac{\alpha\beta a-q}{a-1};\alpha+1-\epsilon,\beta+1-\epsilon,2-\epsilon,% \delta;\frac{a-z}{a-1}\right).}}
    0 references
    DLMF id
    DLMF:31.3.E9
    0 references
    Symbols used
    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.m2aedec
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    Q12457
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C31.S1.XMD1.m1edec
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    Q12458
    Defining formula
    γ 𝛾 {\displaystyle{\displaystyle\gamma}}
    xml-id
    C31.S1.XMD10.m1fdec
    0 references
    Q12459
    Defining formula
    δ 𝛿 {\displaystyle{\displaystyle\delta}}
    xml-id
    C31.S1.XMD11.m1fdec
    0 references
    Q12460
    Defining formula
    ϵ italic-ϵ {\displaystyle{\displaystyle\epsilon}}
    xml-id
    C31.S1.XMD12.m1ddec
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    Q12461
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C31.S1.XMD6.m1gdec
    0 references
    Q12462
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C31.S1.XMD7.m1gdec
    0 references
     
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