General linear differential equation of order n (Q2136): Difference between revisions
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Added content item: General linear differential equation of order n |
Added content item: General linear differential equation of order n |
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| Property / instance of | |||
| Property / instance of: mathematical expression / rank | |||
| Property / LaTeX source | |||
| Property / LaTeX source: \\sum_{|\\alpha|\\le m} a_\\alpha(\\mathbf{x})\\,D^\\alpha u(\\mathbf{x})=f(\\mathbf{x}),\n\\qquad \n\\mathbf{x}=(x_1,\\dots,x_d). / rank | |||
| Property / note | |||
| Property / note: Where:\n\n$a_\\alpha(\\mathbf{x})$ is a function of $\\mathbf{x}$,\n\n$$\n\\alpha=(\\alpha_1,\\dots,\\alpha_d),\n\\qquad \n|\\alpha|=\\alpha_1+\\cdots+\\alpha_d,\n$$\n\nand \n\n$$\nD^\\alpha u=\n\\frac{\\partial^{|\\alpha|}u}\n{\\partial x_1^{\\alpha_1}\\cdots \\partial x_d^{\\alpha_d}}.\n$$ / rank | |||
| Property / attributed to | |||
| Property / attributed to: Rong Martin-Siebler ZHOU / rank | |||
| Property / instance of | |||
| Property / instance of: mathematical expression / rank | |||
Normal rank | |||
| Property / LaTeX source | |||
\\sum_{|\\alpha|\\le m} a_\\alpha(\\mathbf{x})\\,D^\\alpha u(\\mathbf{x})=f(\\mathbf{x}),\n\\qquad \n\\mathbf{x}=(x_1,\\dots,x_d). | |||
| Property / LaTeX source: \\sum_{|\\alpha|\\le m} a_\\alpha(\\mathbf{x})\\,D^\\alpha u(\\mathbf{x})=f(\\mathbf{x}),\n\\qquad \n\\mathbf{x}=(x_1,\\dots,x_d). / rank | |||
Normal rank | |||
| Property / note | |||
Where:\n\n$a_\\alpha(\\mathbf{x})$ is a function of $\\mathbf{x}$,\n\n$$\n\\alpha=(\\alpha_1,\\dots,\\alpha_d),\n\\qquad \n|\\alpha|=\\alpha_1+\\cdots+\\alpha_d,\n$$\n\nand \n\n$$\nD^\\alpha u=\n\\frac{\\partial^{|\\alpha|}u}\n{\\partial x_1^{\\alpha_1}\\cdots \\partial x_d^{\\alpha_d}}.\n$$ | |||
| Property / note: Where:\n\n$a_\\alpha(\\mathbf{x})$ is a function of $\\mathbf{x}$,\n\n$$\n\\alpha=(\\alpha_1,\\dots,\\alpha_d),\n\\qquad \n|\\alpha|=\\alpha_1+\\cdots+\\alpha_d,\n$$\n\nand \n\n$$\nD^\\alpha u=\n\\frac{\\partial^{|\\alpha|}u}\n{\\partial x_1^{\\alpha_1}\\cdots \\partial x_d^{\\alpha_d}}.\n$$ / rank | |||
Normal rank | |||
| Property / attributed to | |||
| Property / attributed to: Rong Martin-Siebler ZHOU / rank | |||
Normal rank | |||
Revision as of 18:53, 10 October 2026
No description defined
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | General linear differential equation of order n |
No description defined |
Statements
\\sum_{|\\alpha|\\le m} a_\\alpha(\\mathbf{x})\\,D^\\alpha u(\\mathbf{x})=f(\\mathbf{x}),\n\\qquad \n\\mathbf{x}=(x_1,\\dots,x_d).
0 references
Where:\n\n$a_\\alpha(\\mathbf{x})$ is a function of $\\mathbf{x}$,\n\n$$\n\\alpha=(\\alpha_1,\\dots,\\alpha_d),\n\\qquad \n|\\alpha|=\\alpha_1+\\cdots+\\alpha_d,\n$$\n\nand \n\n$$\nD^\\alpha u=\n\\frac{\\partial^{|\\alpha|}u}\n{\\partial x_1^{\\alpha_1}\\cdots \\partial x_d^{\\alpha_d}}.\n$$
0 references