Sandbox - Revision history

Vittorio.capobianco at 17:34, 3 June 2005

2005-06-03T17:34:02Z

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	[[WikiSysop]]		[[WikiSysop]]

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Vittorio.capobianco at 17:29, 3 June 2005

2005-06-03T17:29:12Z

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	[[Pagina di esercitazione]]		[[Pagina di esercitazione]]

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Vittorio.capobianco at 17:25, 3 June 2005

2005-06-03T17:25:35Z

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			[[Pagina di esercitazione]]
	== Pagina di esercitazione ==

Vittorio.capobianco at 17:25, 3 June 2005

2005-06-03T17:25:15Z

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	~~Inset text here !~~
			== Pagina di esercitazione ==

Gabriele.vivinetto at 18:55, 5 April 2005

2005-04-05T18:55:14Z

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	~~{{sandbox}}~~		Inset text here !
	~~[[Image:Example.jpg]]--[[User:132.205.24.42\|132.205.24.42]] 17:21, 5 Apr 2005 (UTC)~~
	~~Useful identity for spherical harmonics:~~

	~~<math>~~
	\frac{{\left( x^2 + y^2 + z^2 \right) }^2\, \left( {\sqrt{\frac{\left( l - m \right) \,\left( l + m \right) } {-1 + 4\,l^2}}}\,\left( \frac{\left( 1 + 2\,l + 2\,n \right) \, \left( {\sqrt{\frac{\left( -1 + l - m \right) \, \left( -1 + l + m \right) }{3 - 8\,l + 4\,l^2}}}\, \left( -1 + 2\,l + 2\,n - 2\,a\,x^2 - 2\,a\,y^2 - 2\,a\,z^2 \right) \, \textrm{Y}_{-2 + l}^{m}(\theta,\phi) + 2\,{\sqrt{\frac{\left( l - m \right) \,\left( l + m \right) } {-1 + 4\,l^2}}}\, \left( n - a\,\left( x^2 + y^2 + z^2 \right) \right) \, \textrm{Y}_{l}^{m}(\theta,\phi) \right) } {x^2 + y^2 + z^2} - 2\,a\,\left( {\sqrt{\frac{\left( -1 + l - m \right) \, \left( -1 + l + m \right) }{3 - 8\,l + 4\,l^2}}}\, \left( 1 + 2\,l + 2\,n - 2\,a\,x^2 - 2\,a\,y^2 - 2\,a\,z^2 \right) \, \textrm{Y}_{-2 + l}^{m}(\theta,\phi) - 2\,{\sqrt{\frac{\left( l - m \right) \,\left( l + m \right) } {-1 + 4\,l^2}}}\, \left( -1 - n + a\,\left( x^2 + y^2 + z^2 \right) \right) \, \textrm{Y}_{l}^{m}(\theta,\phi) \right) \ \right) + 2\,{\sqrt{\frac{\left( 1 + l - m \right) \, \left( 1 + l + m \right) }{3 + 8\,l + 4\,l^2}}}\, \left( \frac{n\,\left( {\sqrt{\frac{\left( 1 + l - m \right) \, \left( 1 + l + m \right) }{3 + 8\,l + 4\,l^2}}}\, \left( 1 + 2\,l + 2\,n - 2\,a\,x^2 - 2\,a\,y^2 - 2\,a\,z^2 \right) \, \textrm{Y}_{l}^{m}(\theta,\phi) + 2\,{\sqrt{\frac{\left( 2 + l - m \right) \, \left( 2 + l + m \right) }{\left( 3 + 2\,l \right) \, \left( 5 + 2\,l \right) }}}\, \left( -1 + n - a\,\left( x^2 + y^2 + z^2 \right) \ \right) \,\textrm{Y}_{2 + l}^{m}(\theta, \phi) \right) }{x^2 + y^2 + z^2} + a\,\left( {\sqrt{\frac{\left( 1 + l - m \right) \, \left( 1 + l + m \right) }{3 + 8\,l + 4\,l^2}}}\, \left( -3 - 2\,l - 2\,n + 2\,a\,x^2 + 2\,a\,y^2 + 2\,a\,z^2 \right) \, \textrm{Y}_{l}^{m}(\theta,\phi) + 2\,{\sqrt{\frac{\left( 2 + l - m \right) \, \left( 2 + l + m \right) }{\left( 3 + 2\,l \right) \, \left( 5 + 2\,l \right) }}}\, \left( -n + a\,\left( x^2 + y^2 + z^2 \right) \right) \, \textrm{Y}_{2 + l}^{m}\theta,\phi) \right) \ \right) \right) }{\left( l^2\,z^2 + l\,\left( x^2\,\left( 1 - 4\,a\,z^2 \right) + y^2\,\left( 1 - 4\,a\,z^2 \right) + z^2\,\left( -1 + 4\,n - 4\,a\,z^2 \right) \right) + 2\,\left( 2\,n^2\,z^2 + a\,{\left( x^2 + y^2 + z^2 \right) }^2\, \left( -1 + 2\,a\,z^2 \right) + n\,\left( y^2 - z^2 - 4\,a\,y^2\,z^2 - 4\,a\,z^4 + x^2\,\left( 1 - 4\,a\,z^2 \right) \right) \right) \right) \, \textrm{Y}_{l}^{m}(\theta,\phi)}
	~~= 1~~

	~~</math>Test~~

Gabriele.vivinetto at 18:54, 5 April 2005

2005-04-05T18:54:00Z

New page

{{sandbox}}
[[Image:Example.jpg]]--[[User:132.205.24.42|132.205.24.42]] 17:21, 5 Apr 2005 (UTC)
Useful identity for spherical harmonics:

<math>
\frac{{\left( x^2 + y^2 + z^2 \right) }^2\, \left( {\sqrt{\frac{\left( l - m \right) \,\left( l + m \right) } {-1 + 4\,l^2}}}\,\left( \frac{\left( 1 + 2\,l + 2\,n \right) \, \left( {\sqrt{\frac{\left( -1 + l - m \right) \, \left( -1 + l + m \right) }{3 - 8\,l + 4\,l^2}}}\, \left( -1 + 2\,l + 2\,n - 2\,a\,x^2 - 2\,a\,y^2 - 2\,a\,z^2 \right) \, \textrm{Y}_{-2 + l}^{m}(\theta,\phi) + 2\,{\sqrt{\frac{\left( l - m \right) \,\left( l + m \right) } {-1 + 4\,l^2}}}\, \left( n - a\,\left( x^2 + y^2 + z^2 \right) \right) \, \textrm{Y}_{l}^{m}(\theta,\phi) \right) } {x^2 + y^2 + z^2} - 2\,a\,\left( {\sqrt{\frac{\left( -1 + l - m \right) \, \left( -1 + l + m \right) }{3 - 8\,l + 4\,l^2}}}\, \left( 1 + 2\,l + 2\,n - 2\,a\,x^2 - 2\,a\,y^2 - 2\,a\,z^2 \right) \, \textrm{Y}_{-2 + l}^{m}(\theta,\phi) - 2\,{\sqrt{\frac{\left( l - m \right) \,\left( l + m \right) } {-1 + 4\,l^2}}}\, \left( -1 - n + a\,\left( x^2 + y^2 + z^2 \right) \right) \, \textrm{Y}_{l}^{m}(\theta,\phi) \right) \ \right) + 2\,{\sqrt{\frac{\left( 1 + l - m \right) \, \left( 1 + l + m \right) }{3 + 8\,l + 4\,l^2}}}\, \left( \frac{n\,\left( {\sqrt{\frac{\left( 1 + l - m \right) \, \left( 1 + l + m \right) }{3 + 8\,l + 4\,l^2}}}\, \left( 1 + 2\,l + 2\,n - 2\,a\,x^2 - 2\,a\,y^2 - 2\,a\,z^2 \right) \, \textrm{Y}_{l}^{m}(\theta,\phi) + 2\,{\sqrt{\frac{\left( 2 + l - m \right) \, \left( 2 + l + m \right) }{\left( 3 + 2\,l \right) \, \left( 5 + 2\,l \right) }}}\, \left( -1 + n - a\,\left( x^2 + y^2 + z^2 \right) \ \right) \,\textrm{Y}_{2 + l}^{m}(\theta, \phi) \right) }{x^2 + y^2 + z^2} + a\,\left( {\sqrt{\frac{\left( 1 + l - m \right) \, \left( 1 + l + m \right) }{3 + 8\,l + 4\,l^2}}}\, \left( -3 - 2\,l - 2\,n + 2\,a\,x^2 + 2\,a\,y^2 + 2\,a\,z^2 \right) \, \textrm{Y}_{l}^{m}(\theta,\phi) + 2\,{\sqrt{\frac{\left( 2 + l - m \right) \, \left( 2 + l + m \right) }{\left( 3 + 2\,l \right) \, \left( 5 + 2\,l \right) }}}\, \left( -n + a\,\left( x^2 + y^2 + z^2 \right) \right) \, \textrm{Y}_{2 + l}^{m}\theta,\phi) \right) \ \right) \right) }{\left( l^2\,z^2 + l\,\left( x^2\,\left( 1 - 4\,a\,z^2 \right) + y^2\,\left( 1 - 4\,a\,z^2 \right) + z^2\,\left( -1 + 4\,n - 4\,a\,z^2 \right) \right) + 2\,\left( 2\,n^2\,z^2 + a\,{\left( x^2 + y^2 + z^2 \right) }^2\, \left( -1 + 2\,a\,z^2 \right) + n\,\left( y^2 - z^2 - 4\,a\,y^2\,z^2 - 4\,a\,z^4 + x^2\,\left( 1 - 4\,a\,z^2 \right) \right) \right) \right) \, \textrm{Y}_{l}^{m}(\theta,\phi)}
= 1

</math>Test