DLMF:2.3.E28 (Q748)

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DLMF:2.3.E28
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    Statements

    Defining formula
    d w d t = ± 1 ( 2 ⁢ p ⁢ ( α , t ) - 2 ⁢ p ⁢ ( α , α ) ) 1 / 2 ⁢ ∂ ⁡ p ⁢ ( α , t ) ∂ ⁡ t derivative 𝑤 𝑡 plus-or-minus 1 superscript 2 𝑝 𝛼 𝑡 2 𝑝 𝛼 𝛼 1 2 partial-derivative 𝑝 𝛼 𝑡 𝑡 {\displaystyle{\displaystyle\frac{\mathrm{d}w}{\mathrm{d}t}=\pm\frac{1}{(2p(% \alpha,t)-2p(\alpha,\alpha))^{1/2}}\frac{\partial p(\alpha,t)}{\partial t}}}
    0 references
    DLMF id
    DLMF:2.3.E28
    0 references
    Symbols used
    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.m2aadec
    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.m4adec
    0 references
    partial differential of $$x$$
    Defining formula
    ∂ ⁡ x 𝑥 {\displaystyle{\displaystyle\partial\NVar{x}}}
    xml-id
    C1.S5.E3.m2adec
    0 references
    Q10964
    Defining formula
    p ⁢ ( α , t ) 𝑝 𝛼 𝑡 {\displaystyle{\displaystyle p(\alpha,t)}}
    xml-id
    C2.S3.XMD28.m1ddec
    0 references
    Q10966
    Defining formula
    w 𝑤 {\displaystyle{\displaystyle w}}
    xml-id
    C2.S3.XMD30.m1bdec
    0 references
     
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