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

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
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
 
Defining formula:

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

Revision as of 13:26, 2 January 2020

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DLMF:31.2.E6
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    Statements

    Defining formula
    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
    Defining formula
    cot ⁡ z 𝑧 {\displaystyle{\displaystyle\cot\NVar{z}}}
    xml-id
    C4.S14.E7.m2adec
    0 references
    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.m2abdec
    0 references
     
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