DLMF:31.14.E1 (Q9112): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12477 / rank
 
Normal rank
Property / Symbols used: Q12477 / qualifier
 
test:

j 𝑗 {\displaystyle{\displaystyle j}}

j
Property / Symbols used: Q12477 / qualifier
 
xml-id: C31.S1.XMD2.m1dec
Property / Symbols used
 
Property / Symbols used: Q12461 / rank
 
Normal rank
Property / Symbols used: Q12461 / qualifier
 
test:

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
 
test:

q 𝑞 {\displaystyle{\displaystyle q}}

q
Property / Symbols used: Q12462 / qualifier
 
xml-id: C31.S1.XMD7.m1dec
Property / Symbols used
 
Property / Symbols used: Q12512 / rank
 
Normal rank
Property / Symbols used: Q12512 / qualifier
 
test:

N + 1 𝑁 1 {\displaystyle{\displaystyle N+1}}

N+1
Property / Symbols used: Q12512 / qualifier
 
xml-id: C31.S14.XMD1.m1dec

Latest revision as of 12:42, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:31.14.E1
No description defined

    Statements

    test
    d 2 w d z 2 + ( ∑ j = 1 N γ j z - a j ) ⁢ d w d z + ( ∑ j = 1 N q j z - a j ) ⁢ w = 0 , derivative 𝑤 𝑧 2 superscript subscript 𝑗 1 𝑁 subscript 𝛾 𝑗 𝑧 subscript 𝑎 𝑗 derivative 𝑤 𝑧 superscript subscript 𝑗 1 𝑁 subscript 𝑞 𝑗 𝑧 subscript 𝑎 𝑗 𝑤 0 {\displaystyle{\displaystyle{\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}z}^{2}}+\left% (\sum_{j=1}^{N}\frac{\gamma_{j}}{z-a_{j}}\right)\frac{\mathrm{d}w}{\mathrm{d}z% }+\left(\sum_{j=1}^{N}\frac{q_{j}}{z-a_{j}}\right)w=0},}}
    0 references
    DLMF id
    DLMF:31.14.E1
    0 references
    constraint
    ∑ j = 1 N q j = 0 superscript subscript 𝑗 1 𝑁 subscript 𝑞 𝑗 0 {\displaystyle{\displaystyle\sum_{j=1}^{N}q_{j}=0}}
    0 references
    Symbols used
    derivative of $$f$$ with respect to $$x$$
    test
    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
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C31.S1.XMD1.m1dec
    0 references
    Q12458
    test
    γ 𝛾 {\displaystyle{\displaystyle\gamma}}
    xml-id
    C31.S1.XMD10.m1dec
    0 references
    Q12477
    test
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C31.S1.XMD2.m1dec
    0 references
    Q12461
    test
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C31.S1.XMD6.m1dec
    0 references
    Q12462
    test
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C31.S1.XMD7.m1dec
    0 references
    Q12512
    test
    N + 1 𝑁 1 {\displaystyle{\displaystyle N+1}}
    xml-id
    C31.S14.XMD1.m1dec
    0 references
     
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