DLMF:31.3.E13 (Q9017): 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.m1idec
Property / Symbols used
 
Property / Symbols used: Q12458 / rank
 
Normal rank
Property / Symbols used: Q12458 / qualifier
 
Defining formula:

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

\gamma
Property / Symbols used: Q12458 / qualifier
 
xml-id: C31.S1.XMD10.m1jdec
Property / Symbols used
 
Property / Symbols used: Q12459 / rank
 
Normal rank
Property / Symbols used: Q12459 / qualifier
 
Defining formula:

δ 𝛿 {\displaystyle{\displaystyle\delta}}

\delta
Property / Symbols used: Q12459 / qualifier
 
xml-id: C31.S1.XMD11.m1jdec
Property / Symbols used
 
Property / Symbols used: Q12461 / rank
 
Normal rank
Property / Symbols used: Q12461 / qualifier
 
Defining formula:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q12461 / qualifier
 
xml-id: C31.S1.XMD6.m1kdec
Property / Symbols used
 
Property / Symbols used: Q12462 / rank
 
Normal rank
Property / Symbols used: Q12462 / qualifier
 
Defining formula:

q 𝑞 {\displaystyle{\displaystyle q}}

q
Property / Symbols used: Q12462 / qualifier
 
xml-id: C31.S1.XMD7.m1kdec
Property / Symbols used
 
Property / Symbols used: Q12463 / rank
 
Normal rank
Property / Symbols used: Q12463 / qualifier
 
Defining formula:

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

\alpha
Property / Symbols used: Q12463 / qualifier
 
xml-id: C31.S1.XMD8.m1jdec
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.m1jdec

Latest revision as of 13:30, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:31.3.E13
No description defined

    Statements

    Defining formula
    ( 1 - z ) - α ⁢ H ⁢ ℓ ⁡ ( a a - 1 , - q - a ⁢ α ⁢ γ a - 1 ; α , α + 1 - δ , γ , α + 1 - β ; z z - 1 ) , superscript 1 𝑧 𝛼 Heun-local 𝑎 𝑎 1 𝑞 𝑎 𝛼 𝛾 𝑎 1 𝛼 𝛼 1 𝛿 𝛾 𝛼 1 𝛽 𝑧 𝑧 1 {\displaystyle{\displaystyle(1-z)^{-\alpha}\*\mathit{H\!\ell}\left(\frac{a}{a-% 1},-\frac{q-a\alpha\gamma}{a-1};\alpha,\alpha+1-\delta,\gamma,\alpha+1-\beta;% \frac{z}{z-1}\right),}}
    0 references
    DLMF id
    DLMF:31.3.E13
    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.m2aidec
    0 references
    Q12457
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C31.S1.XMD1.m1idec
    0 references
    Q12458
    Defining formula
    γ 𝛾 {\displaystyle{\displaystyle\gamma}}
    xml-id
    C31.S1.XMD10.m1jdec
    0 references
    Q12459
    Defining formula
    δ 𝛿 {\displaystyle{\displaystyle\delta}}
    xml-id
    C31.S1.XMD11.m1jdec
    0 references
    Q12461
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C31.S1.XMD6.m1kdec
    0 references
    Q12462
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C31.S1.XMD7.m1kdec
    0 references
    Q12463
    Defining formula
    α 𝛼 {\displaystyle{\displaystyle\alpha}}
    xml-id
    C31.S1.XMD8.m1jdec
    0 references
    Q12464
    Defining formula
    β 𝛽 {\displaystyle{\displaystyle\beta}}
    xml-id
    C31.S1.XMD9.m1jdec
    0 references
     
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