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List of Equations

The database contains 327 equations (8 equations are awaiting activation).

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See also: Categorized List of Equations

6. Difference and Functional Equations

6.3. Linear Equations in Two and More Independent Variables

Found 9 equations
 Equation(s)Author/
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1 \noindent
$\displaystyle w(x,y)=a^ne^{bm}w(ax,y+b)$,\hfill\break
where $a$ and $b$ are arbitrary parameters ($a>0$). Andrei Polyanin
Submitted: 06 Dec 06 11:45
Edited (author): 11 Dec 06 12:42
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2 \noindent
$\displaystyle w(x,y)=e^{ak+bm}w(x+a,y+b)$,\hfill\break
where $a$ and $b$ are arbitrary parameters. Andrei Polyanin
Submitted: 06 Dec 06 11:51
Edited (author): 11 Dec 06 12:43
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3 \noindent
$w(x,y)=a^nb^mw(ax,by)$,\hfill\break 
where $a>0$ and $b>0$ are arbitrary parameters. Andrei Polyanin
Submitted: 30 Nov 06 13:43
Edited (author): 11 Dec 06 12:45
Edited (admin): 06 Dec 06 12:47
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4 \noindent
$\displaystyle w(x,y)=w(ay,x/a)$,\hfill\break
where $a\not=0$ is an arbitrary parameter. Andrei Polyanin
Submitted: 06 Dec 06 11:56
Edited (author): 11 Dec 06 12:45
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5 $\displaystyle w(x,y,z)=w(ax,by,a^nb^mz)$,\hfill\break
where $a$ and $b$ are arbitrary numbers ($a,b>0$). Andrei Polyanin
Submitted: 23 Aug 07 10:21
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6 \noindent
$w(x,y)=w(y+a,x-a)$,\hfill\break
where $a$ is an arbitrary parameter. Andrei Polyanin
Submitted: 30 Nov 06 13:29
Edited (author): 11 Dec 06 12:44
Edited (admin): 22 Sep 08 09:29
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7 $ w(x,y)=w(ay,ax)$,\hfill\break
where $a\not=0$ is an arbitrary constant. Andrei Polyanin
Submitted: 22 Sep 08 09:14
Edited (admin): 22 Sep 08 09:31
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8 $w(x,y)=w(y+a,x+a)$,\hfill\break
where $a$ is an arbitrary constant. Andrei Polyanin
Submitted: 22 Sep 08 09:20
Edited (admin): 22 Sep 08 09:34
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9 $f(x,y)-f(x,b)-f(a,y)+f(a,b)=0$. Andrei Polyanin
Submitted: 10 Feb 10 16:15
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Found 9 equations

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