DLMF:3.4.E24 (Q1228): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: partial differential of $$x$$ / rank
 
Normal rank
Property / Symbols used: partial differential of $$x$$ / qualifier
 
Defining formula:

∂ ⁡ x 𝑥 {\displaystyle{\displaystyle\partial\NVar{x}}}

\pdiff{\NVar{x}}
Property / Symbols used: partial differential of $$x$$ / qualifier
 
xml-id: C1.S5.E3.m2addec

Revision as of 17:48, 1 January 2020

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DLMF:3.4.E24
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    Statements

    Defining formula
    ∂ 2 ⁡ u 0 , 0 ∂ ⁡ x 2 = 1 3 ⁢ h 2 ⁢ ( u 1 , 1 - 2 ⁢ u 0 , 1 + u - 1 , 1 + u 1 , 0 - 2 ⁢ u 0 , 0 + u - 1 , 0 + u 1 , - 1 - 2 ⁢ u 0 , - 1 + u - 1 , - 1 ) + O ⁡ ( h 2 ) . partial-derivative subscript 𝑢 0 0 𝑥 2 1 3 superscript ℎ 2 subscript 𝑢 1 1 2 subscript 𝑢 0 1 subscript 𝑢 1 1 subscript 𝑢 1 0 2 subscript 𝑢 0 0 subscript 𝑢 1 0 subscript 𝑢 1 1 2 subscript 𝑢 0 1 subscript 𝑢 1 1 Big-O superscript ℎ 2 {\displaystyle{\displaystyle\frac{{\partial}^{2}u_{0,0}}{{\partial x}^{2}}=% \frac{1}{3h^{2}}\,(u_{1,1}-2u_{0,1}+u_{-1,1}+u_{1,0}-2u_{0,0}+u_{-1,0}+u_{1,-1% }-2u_{0,-1}+u_{-1,-1})+O\left(h^{2}\right).}}
    0 references
    DLMF id
    DLMF:3.4.E24
    0 references
    Symbols used
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2addec
    0 references
    partial derivative of $$f$$ with respect to $$x$$
    Defining formula
    ∂ ⁡ f ∂ ⁡ x partial-derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}
    xml-id
    C1.S5.E3.m4addec
    0 references
    partial differential of $$x$$
    Defining formula
    ∂ ⁡ x 𝑥 {\displaystyle{\displaystyle\partial\NVar{x}}}
    xml-id
    C1.S5.E3.m2addec
    0 references
     
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