DLMF:31.2.E1 (Q8976): 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.m1dec
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.m1dec
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.m1dec
Property / Symbols used
 
Property / Symbols used: Q12460 / rank
 
Normal rank
Property / Symbols used: Q12460 / qualifier
 
Defining formula:

ϵ italic-ϵ {\displaystyle{\displaystyle\epsilon}}

\epsilon
Property / Symbols used: Q12460 / qualifier
 
xml-id: C31.S1.XMD12.m1dec
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.m1dec
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.m1dec
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.m1dec
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.m1dec

Latest revision as of 13:25, 2 January 2020

No description defined
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English
DLMF:31.2.E1
No description defined

    Statements

    Defining formula
    d 2 w d z 2 + ( γ z + δ z - 1 + ϵ z - a ) ⁢ d w d z + α ⁢ β ⁢ z - q z ⁢ ( z - 1 ) ⁢ ( z - a ) ⁢ w = 0 , derivative 𝑤 𝑧 2 𝛾 𝑧 𝛿 𝑧 1 italic-ϵ 𝑧 𝑎 derivative 𝑤 𝑧 𝛼 𝛽 𝑧 𝑞 𝑧 𝑧 1 𝑧 𝑎 𝑤 0 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}z}^{2}}+\left(% \frac{\gamma}{z}+\frac{\delta}{z-1}+\frac{\epsilon}{z-a}\right)\frac{\mathrm{d% }w}{\mathrm{d}z}+\frac{\alpha\beta z-q}{z(z-1)(z-a)}w=0,}}
    0 references
    DLMF id
    DLMF:31.2.E1
    0 references
    constraint
    α + β + 1 = γ + δ + ϵ 𝛼 𝛽 1 𝛾 𝛿 italic-ϵ {\displaystyle{\displaystyle\alpha+\beta+1=\gamma+\delta+\epsilon}}
    0 references
    Symbols used
    derivative of $$f$$ with respect to $$x$$
    Defining formula
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2adec
    0 references
    Q12457
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C31.S1.XMD1.m1dec
    0 references
    Q12458
    Defining formula
    γ 𝛾 {\displaystyle{\displaystyle\gamma}}
    xml-id
    C31.S1.XMD10.m1dec
    0 references
    Q12459
    Defining formula
    δ 𝛿 {\displaystyle{\displaystyle\delta}}
    xml-id
    C31.S1.XMD11.m1dec
    0 references
    Q12460
    Defining formula
    ϵ italic-ϵ {\displaystyle{\displaystyle\epsilon}}
    xml-id
    C31.S1.XMD12.m1dec
    0 references
    Q12461
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C31.S1.XMD6.m1dec
    0 references
    Q12462
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C31.S1.XMD7.m1dec
    0 references
    Q12463
    Defining formula
    α 𝛼 {\displaystyle{\displaystyle\alpha}}
    xml-id
    C31.S1.XMD8.m1dec
    0 references
    Q12464
    Defining formula
    β 𝛽 {\displaystyle{\displaystyle\beta}}
    xml-id
    C31.S1.XMD9.m1dec
    0 references
     
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