DLMF:36.11.E2 (Q9985): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:36.11.E2	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\Psi_{K}\left(\mathbf{x}\right)=\sqrt{2\pi}\sum% \limits_{j=1}^{j_{\max}(\mathbf{x})}\exp\left(i\left(\Phi_{K}\left(t_{j}(% \mathbf{x});\mathbf{x}\right)+\tfrac{1}{4}\pi(-1)^{j+K+1}\right)\right)\left|% \frac{{\partial}^{2}\Phi_{K}\left(t_{j}(\mathbf{x});\mathbf{x}\right)}{{% \partial t}^{2}}\right|^{-1/2}(1+o\left(1\right)).}}

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DLMF:36.11.E2

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canonical integral function

Defining formula

{\displaystyle{\displaystyle\Psi_{\NVar{K}}\left(\NVar{\mathbf{x}}\right)}}

C36.S2.E4.m2adec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2adec

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cuspoid catastrophe of codimension $$K$$

Defining formula

{\displaystyle{\displaystyle\Phi_{\NVar{K}}\left(\NVar{t};\NVar{\mathbf{x}}% \right)}}

C36.S2.E1.m2adec

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exponential function

Defining formula

{\displaystyle{\displaystyle\exp\NVar{z}}}

C4.S2.E19.m2adec

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Defining formula

{\displaystyle{\displaystyle\mathrm{i}}}

C1.S9.E1.m2adec

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order less than

Defining formula

{\displaystyle{\displaystyle o\left(\NVar{x}\right)}}

C2.S1.E2.m2adec

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partial derivative of $$f$$ with respect to $$x$$

Defining formula

{\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}

C1.S5.E3.m4adec

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partial differential of $$x$$

Defining formula

{\displaystyle{\displaystyle\partial\NVar{x}}}

C1.S5.E3.m2adec

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Defining formula

{\displaystyle{\displaystyle t}}

C36.S1.XMD5.m1dec

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Defining formula

{\displaystyle{\displaystyle K}}

C36.S1.XMD7.m1dec

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Defining formula

{\displaystyle{\displaystyle t_{j}(\mathbf{x})}}

C36.S4.XMD1.m1adec

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