DLMF:36.12.E4 (Q9995)

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DLMF:36.12.E4
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    Statements

    Defining formula
    f ⁢ ( u ⁢ ( t , 𝐲 ) ; 𝐲 ) = A ⁢ ( 𝐲 ) + Φ K ⁡ ( t ; 𝐱 ⁢ ( 𝐲 ) ) , 𝑓 𝑢 𝑡 𝐲 𝐲 𝐴 𝐲 cuspoid-catastrophe 𝐾 𝑡 𝐱 𝐲 {\displaystyle{\displaystyle f(u(t,\mathbf{y});\mathbf{y})=A(\mathbf{y})+\Phi_% {K}\left(t;\mathbf{x}(\mathbf{y})\right),}}
    0 references
    DLMF id
    DLMF:36.12.E4
    0 references
    Symbols used
    cuspoid catastrophe of codimension $$K$$
    Defining formula
    Φ K ⁡ ( t ; 𝐱 ) cuspoid-catastrophe 𝐾 𝑡 𝐱 {\displaystyle{\displaystyle\Phi_{\NVar{K}}\left(\NVar{t};\NVar{\mathbf{x}}% \right)}}
    xml-id
    C36.S2.E1.m2adec
    0 references
    Q12742
    Defining formula
    t 𝑡 {\displaystyle{\displaystyle t}}
    xml-id
    C36.S1.XMD5.m1dec
    0 references
    Q12743
    Defining formula
    K 𝐾 {\displaystyle{\displaystyle K}}
    xml-id
    C36.S1.XMD7.m1adec
    0 references
    Q12760
    Defining formula
    f ⁢ ( u , 𝐲 ) 𝑓 𝑢 𝐲 {\displaystyle{\displaystyle f(u,\mathbf{y})}}
    xml-id
    C36.S12.XMD3.m1bdec
    0 references
    function (locally)
    Defining formula
    A ⁢ ( 𝐲 ) 𝐴 𝐲 {\displaystyle{\displaystyle A(\mathbf{y})}}
    xml-id
    C36.S12.XMD7.m1adec
    0 references
     
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