DLMF:31.7.E2 (Q9025): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12457 / rank
 
Normal rank
Property / Symbols used: Q12457 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q12457 / qualifier
 
xml-id: C31.S1.XMD1.m1adec
Property / Symbols used
 
Property / Symbols used: Q12458 / rank
 
Normal rank
Property / Symbols used: Q12458 / qualifier
 
test:

γ 𝛾 {\displaystyle{\displaystyle\gamma}}

\gamma
Property / Symbols used: Q12458 / qualifier
 
xml-id: C31.S1.XMD10.m1adec
Property / Symbols used
 
Property / Symbols used: Q12463 / rank
 
Normal rank
Property / Symbols used: Q12463 / qualifier
 
test:

α 𝛼 {\displaystyle{\displaystyle\alpha}}

\alpha
Property / Symbols used: Q12463 / qualifier
 
xml-id: C31.S1.XMD8.m1adec
Property / Symbols used
 
Property / Symbols used: Q12464 / rank
 
Normal rank
Property / Symbols used: Q12464 / qualifier
 
test:

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

\beta
Property / Symbols used: Q12464 / qualifier
 
xml-id: C31.S1.XMD9.m1adec

Latest revision as of 12:32, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:31.7.E2
No description defined

    Statements

    test
    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
    test
    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
    Heun functions
    test
    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.m2aadec
    0 references
    Q12457
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C31.S1.XMD1.m1adec
    0 references
    Q12458
    test
    γ 𝛾 {\displaystyle{\displaystyle\gamma}}
    xml-id
    C31.S1.XMD10.m1adec
    0 references
    Q12463
    test
    α 𝛼 {\displaystyle{\displaystyle\alpha}}
    xml-id
    C31.S1.XMD8.m1adec
    0 references
    Q12464
    test
    β 𝛽 {\displaystyle{\displaystyle\beta}}
    xml-id
    C31.S1.XMD9.m1adec
    0 references
     
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