DLMF:31.3.E7 (Q9011): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12464 / rank
 
Normal rank
Property / Symbols used: Q12464 / qualifier
 
Defining formula:

β 𝛽 {\displaystyle{\displaystyle\beta}}

\beta
Property / Symbols used: Q12464 / qualifier
 
xml-id: C31.S1.XMD9.m1ddec

Latest revision as of 13:28, 2 January 2020

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English
DLMF:31.3.E7
No description defined

    Statements

    Defining formula
    ( 1 - z ) 1 - δ ⁢ H ⁢ ℓ ⁡ ( 1 - a , ( ( 1 - a ) ⁢ γ + ϵ ) ⁢ ( 1 - δ ) + α ⁢ β - q ; α + 1 - δ , β + 1 - δ , 2 - δ , γ ; 1 - z ) . superscript 1 𝑧 1 𝛿 Heun-local 1 𝑎 1 𝑎 𝛾 italic-ϵ 1 𝛿 𝛼 𝛽 𝑞 𝛼 1 𝛿 𝛽 1 𝛿 2 𝛿 𝛾 1 𝑧 {\displaystyle{\displaystyle(1-z)^{1-\delta}\*\mathit{H\!\ell}\left(1-a,((1-a)% \gamma+\epsilon)(1-\delta)+\alpha\beta-q;\alpha+1-\delta,\beta+1-\delta,2-% \delta,\gamma;1-z\right).}}
    0 references
    DLMF id
    DLMF:31.3.E7
    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.m2acdec
    0 references
    Q12457
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C31.S1.XMD1.m1cdec
    0 references
    Q12458
    Defining formula
    γ 𝛾 {\displaystyle{\displaystyle\gamma}}
    xml-id
    C31.S1.XMD10.m1edec
    0 references
    Q12459
    Defining formula
    δ 𝛿 {\displaystyle{\displaystyle\delta}}
    xml-id
    C31.S1.XMD11.m1ddec
    0 references
    Q12460
    Defining formula
    ϵ italic-ϵ {\displaystyle{\displaystyle\epsilon}}
    xml-id
    C31.S1.XMD12.m1bdec
    0 references
    Q12461
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C31.S1.XMD6.m1edec
    0 references
    Q12462
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C31.S1.XMD7.m1edec
    0 references
    Q12463
    Defining formula
    α 𝛼 {\displaystyle{\displaystyle\alpha}}
    xml-id
    C31.S1.XMD8.m1ddec
    0 references
    Q12464
    Defining formula
    β 𝛽 {\displaystyle{\displaystyle\beta}}
    xml-id
    C31.S1.XMD9.m1ddec
    0 references
     
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