DLMF:31.2.E6 (Q8986): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / rank
 
Normal rank
Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / qualifier
 
test:

d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}

\deriv{\NVar{f}}{\NVar{x}}
Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / qualifier
 
xml-id: C1.S4.E4.m2abdec
Property / Symbols used
 
Property / Symbols used: sine function / rank
 
Normal rank
Property / Symbols used: sine function / qualifier
 
test:

sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}

\sin@@{\NVar{z}}
Property / Symbols used: sine function / qualifier
 
xml-id: C4.S14.E1.m2aadec
Property / Symbols used
 
Property / Symbols used: tangent function / rank
 
Normal rank
Property / Symbols used: tangent function / qualifier
 
test:

tan ⁡ z 𝑧 {\displaystyle{\displaystyle\tan\NVar{z}}}

\tan@@{\NVar{z}}
Property / Symbols used: tangent function / qualifier
 
xml-id: C4.S14.E4.m2adec
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.m1cdec
Property / Symbols used
 
Property / Symbols used: Q12459 / rank
 
Normal rank
Property / Symbols used: Q12459 / qualifier
 
test:

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

\delta
Property / Symbols used: Q12459 / qualifier
 
xml-id: C31.S1.XMD11.m1cdec
Property / Symbols used
 
Property / Symbols used: Q12460 / rank
 
Normal rank
Property / Symbols used: Q12460 / qualifier
 
test:

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

\epsilon
Property / Symbols used: Q12460 / qualifier
 
xml-id: C31.S1.XMD12.m1cdec
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.m1ddec
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.m1bdec
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.m1bdec

Latest revision as of 12:26, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:31.2.E6
No description defined

    Statements

    test
    d 2 w d θ 2 + ( ( 2 ⁢ γ - 1 ) ⁢ cot ⁡ θ - ( 2 ⁢ δ - 1 ) ⁢ tan ⁡ θ - ϵ ⁢ sin ⁡ ( 2 ⁢ θ ) a - sin 2 ⁡ θ ) ⁢ d w d θ + 4 ⁢ α ⁢ β ⁢ sin 2 ⁡ θ - q a - sin 2 ⁡ θ ⁢ w = 0 . derivative 𝑤 𝜃 2 2 𝛾 1 𝜃 2 𝛿 1 𝜃 italic-ϵ 2 𝜃 𝑎 2 𝜃 derivative 𝑤 𝜃 4 𝛼 𝛽 2 𝜃 𝑞 𝑎 2 𝜃 𝑤 0 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}\theta}^{2}}+% \left({(2\gamma-1)\cot\theta-(2\delta-1)\tan\theta}-\frac{\epsilon\sin\left(2% \theta\right)}{a-{\sin^{2}}\theta}\right)\frac{\mathrm{d}w}{\mathrm{d}\theta}+% 4\frac{\alpha\beta{\sin^{2}}\theta-q}{a-{\sin^{2}}\theta}w=0.}}
    0 references
    DLMF id
    DLMF:31.2.E6
    0 references
    Symbols used
    cotangent function
    test
    cot ⁡ z 𝑧 {\displaystyle{\displaystyle\cot\NVar{z}}}
    xml-id
    C4.S14.E7.m2adec
    0 references
    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.m2abdec
    0 references
    sine function
    test
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2aadec
    0 references
    tangent function
    test
    tan ⁡ z 𝑧 {\displaystyle{\displaystyle\tan\NVar{z}}}
    xml-id
    C4.S14.E4.m2adec
    0 references
    Q12458
    test
    γ 𝛾 {\displaystyle{\displaystyle\gamma}}
    xml-id
    C31.S1.XMD10.m1cdec
    0 references
    Q12459
    test
    δ 𝛿 {\displaystyle{\displaystyle\delta}}
    xml-id
    C31.S1.XMD11.m1cdec
    0 references
    Q12460
    test
    ϵ italic-ϵ {\displaystyle{\displaystyle\epsilon}}
    xml-id
    C31.S1.XMD12.m1cdec
    0 references
    Q12461
    test
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C31.S1.XMD6.m1ddec
    0 references
    Q12462
    test
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C31.S1.XMD7.m1bdec
    0 references
    Q12463
    test
    α 𝛼 {\displaystyle{\displaystyle\alpha}}
    xml-id
    C31.S1.XMD8.m1bdec
    0 references
     
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