Item:Q2136 - Revision history

Rongzhou: Updated the item for General linear differential equation of order n from Special:Update

2026-10-10T20:28:48Z

Updated the item for General linear differential equation of order n from Special:Update

← Older revision		Revision as of 20:28, 10 October 2026
Property / instance of
	~~mathematical expression~~
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$a_\\alpha(\\mathbf{x})$ and $f(\\mathbf{x})$ are functions 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$a_\\alpha(\\mathbf{x})$ and $f(\\mathbf{x})$ are functions 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
	~~Rong Martin-Siebler ZHOU~~
Property / attributed to: Rong Martin-Siebler ZHOU / rank
	~~Normal rank~~
		Property / instance of
			mathematical expression
		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$a_\\alpha(\\mathbf{x})$ and $f(\\mathbf{x})$ are functions 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$a_\\alpha(\\mathbf{x})$ and $f(\\mathbf{x})$ are functions 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
			Rong Martin-Siebler ZHOU
		Property / attributed to: Rong Martin-Siebler ZHOU / rank
			Normal rank

Rongzhou: Updated the item for General linear differential equation of order n from Special:Update

2026-10-10T19:33:04Z

Updated the item for General linear differential equation of order n from Special:Update

← Older revision		Revision as of 19:33, 10 October 2026
Property / instance of
	~~mathematical expression~~
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
	~~Rong Martin-Siebler ZHOU~~
Property / attributed to: Rong Martin-Siebler ZHOU / rank
	~~Normal rank~~
		Property / instance of
			mathematical expression
		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$a_\\alpha(\\mathbf{x})$ and $f(\\mathbf{x})$ are functions 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$a_\\alpha(\\mathbf{x})$ and $f(\\mathbf{x})$ are functions 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
			Rong Martin-Siebler ZHOU
		Property / attributed to: Rong Martin-Siebler ZHOU / rank
			Normal rank

Rongzhou: Added content item: General linear differential equation of order n

2026-10-10T18:53:21Z

Added content item: General linear differential equation of order n

← Older revision		Revision as of 18:53, 10 October 2026
Property / instance of
	~~mathematical expression~~
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
	~~Rong Martin-Siebler ZHOU~~
Property / attributed to: Rong Martin-Siebler ZHOU / rank
	~~Normal rank~~
		Property / instance of
			mathematical expression
		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
			Rong Martin-Siebler ZHOU
		Property / attributed to: Rong Martin-Siebler ZHOU / rank
			Normal rank

Rongzhou: Added content item: General linear differential equation of order n

2026-10-10T18:53:21Z

Added content item: General linear differential equation of order n

Show changes