DLMF:3.4.E30 (Q1234): 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.m2ahdec

Revision as of 17:49, 1 January 2020

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DLMF:3.4.E30
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    Statements

    Defining formula
    ∂ 4 ⁡ u 0 , 0 ∂ ⁡ x 4 = 1 h 4 ⁢ ( u 2 , 0 - 4 ⁢ u 1 , 0 + 6 ⁢ u 0 , 0 - 4 ⁢ u - 1 , 0 + u - 2 , 0 ) + O ⁡ ( h 2 ) . partial-derivative subscript 𝑢 0 0 𝑥 4 1 superscript ℎ 4 subscript 𝑢 2 0 4 subscript 𝑢 1 0 6 subscript 𝑢 0 0 4 subscript 𝑢 1 0 subscript 𝑢 2 0 Big-O superscript ℎ 2 {\displaystyle{\displaystyle\frac{{\partial}^{4}u_{0,0}}{{\partial x}^{4}}=% \frac{1}{h^{4}}\,(u_{2,0}-4u_{1,0}+6u_{0,0}-4u_{-1,0}+u_{-2,0})+O\left(h^{2}% \right).}}
    0 references
    DLMF id
    DLMF:3.4.E30
    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.m2aidec
    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.m4afdec
    0 references
    partial differential of $$x$$
    Defining formula
    ∂ ⁡ x 𝑥 {\displaystyle{\displaystyle\partial\NVar{x}}}
    xml-id
    C1.S5.E3.m2ahdec
    0 references
     
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