DLMF:2.4.E20 (Q775)

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DLMF:2.4.E20
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    Statements

    Defining formula
    f ⁢ ( α , w ) = q ⁢ ( α , t ) ⁢ d t d w = q ⁢ ( α , t ) ⁢ w 2 + 2 ⁢ a ⁢ w + b ∂ ⁡ p ⁢ ( α , t ) / ∂ ⁡ t . 𝑓 𝛼 𝑤 𝑞 𝛼 𝑡 derivative 𝑡 𝑤 𝑞 𝛼 𝑡 superscript 𝑤 2 2 𝑎 𝑤 𝑏 partial-derivative 𝑝 𝛼 𝑡 𝑡 {\displaystyle{\displaystyle f(\alpha,w)=q(\alpha,t)\frac{\mathrm{d}t}{\mathrm% {d}w}=q(\alpha,t)\frac{w^{2}+2aw+b}{\ifrac{\partial p(\alpha,t)}{\partial t}}.}}
    0 references
    DLMF id
    DLMF:2.4.E20
    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.m2adec
    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
    Q10981
    Defining formula
    p ⁢ ( t ) 𝑝 𝑡 {\displaystyle{\displaystyle p(t)}}
    xml-id
    C2.S4.XMD15.m1hdec
    0 references
    Q10973
    Defining formula
    q ⁢ ( t ) 𝑞 𝑡 {\displaystyle{\displaystyle q(t)}}
    xml-id
    C2.S4.XMD16.m1mdec
    0 references
    Q10987
    Defining formula
    w 𝑤 {\displaystyle{\displaystyle w}}
    xml-id
    C2.S4.XMD21.m1bdec
    0 references
    Q10988
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C2.S4.XMD22.m1bdec
    0 references
    Q10989
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C2.S4.XMD23.m1bdec
    0 references
    Q10991
    Defining formula
    f ⁢ ( α , w ) 𝑓 𝛼 𝑤 {\displaystyle{\displaystyle f(\alpha,w)}}
    xml-id
    C2.S4.XMD26.m1adec
    0 references
     
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