DLMF:31.7.E3 (Q9026): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12457 / rank
 
Normal rank
Property / Symbols used: Q12457 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q12457 / qualifier
 
xml-id: C31.S1.XMD1.m1bdec

Revision as of 13:32, 2 January 2020

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DLMF:31.7.E3
No description defined

    Statements

    Defining formula
    H ⁢ ℓ ⁡ ( 4 , α ⁢ β ; α , β , 1 2 , 2 3 ⁢ ( α + β ) ; z ) = F 1 2 ⁡ ( 1 3 ⁢ α , 1 3 ⁢ β ; 1 2 ; 1 - ( 1 - z ) 2 ⁢ ( 1 - 1 4 ⁢ z ) ) , Heun-local 4 𝛼 𝛽 𝛼 𝛽 1 2 2 3 𝛼 𝛽 𝑧 Gauss-hypergeometric-F-as-2F1 1 3 𝛼 1 3 𝛽 1 2 1 superscript 1 𝑧 2 1 1 4 𝑧 {\displaystyle{\displaystyle\mathit{H\!\ell}\left(4,\alpha\beta;\alpha,\beta,% \tfrac{1}{2},\tfrac{2}{3}(\alpha+\beta);z\right)={{}_{2}F_{1}}\left(\tfrac{1}{% 3}\alpha,\tfrac{1}{3}\beta;\tfrac{1}{2};1-(1-z)^{2}(1-\tfrac{1}{4}z)\right),}}
    0 references
    DLMF id
    DLMF:31.7.E3
    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.m5abdec
    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.m2abdec
    0 references
    Q12457
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C31.S1.XMD1.m1bdec
    0 references
     
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