DLMF:3.4.E22 (Q1226): Difference between revisions

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

∂ ⁡ f ∂ ⁡ x partial-derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}

\pderiv{\NVar{f}}{\NVar{x}}
Property / Symbols used: partial derivative of $$f$$ with respect to $$x$$ / qualifier
 
xml-id: C1.S5.E3.m4abdec
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.m2abdec
Property / Symbols used
 
Property / Symbols used: Q11166 / rank
 
Normal rank
Property / Symbols used: Q11166 / qualifier
 
Defining formula:

u 𝑢 {\displaystyle{\displaystyle u}}

u
Property / Symbols used: Q11166 / qualifier
 
xml-id: C3.S4.XMD6.m1bdec

Latest revision as of 17:48, 1 January 2020

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DLMF:3.4.E22
No description defined

    Statements

    Defining formula
    ∂ 2 ⁡ u 0 , 0 ∂ ⁡ x 2 = 1 h 2 ⁢ ( u 1 , 0 - 2 ⁢ u 0 , 0 + u - 1 , 0 ) + O ⁡ ( h 2 ) , partial-derivative subscript 𝑢 0 0 𝑥 2 1 superscript ℎ 2 subscript 𝑢 1 0 2 subscript 𝑢 0 0 subscript 𝑢 1 0 Big-O superscript ℎ 2 {\displaystyle{\displaystyle\frac{{\partial}^{2}u_{0,0}}{{\partial x}^{2}}=% \frac{1}{h^{2}}\,(u_{1,0}-2u_{0,0}+u_{-1,0})+O\left(h^{2}\right),}}
    0 references
    DLMF id
    DLMF:3.4.E22
    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.m2abdec
    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.m4abdec
    0 references
    partial differential of $$x$$
    Defining formula
    ∂ ⁡ x 𝑥 {\displaystyle{\displaystyle\partial\NVar{x}}}
    xml-id
    C1.S5.E3.m2abdec
    0 references
    Q11166
    Defining formula
    u 𝑢 {\displaystyle{\displaystyle u}}
    xml-id
    C3.S4.XMD6.m1bdec
    0 references
     
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