## [Maxima-bugs] [ maxima-Bugs-3411198 ] spherical_harmonic switches phase for odd values of m

 [Maxima-bugs] [ maxima-Bugs-3411198 ] spherical_harmonic switches phase for odd values of m From: SourceForge.net - 2011-09-18 11:40:18 ```Bugs item #3411198, was opened at 2011-09-18 13:40 Message generated for change (Tracker Item Submitted) made by maximuser You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3411198&group_id=4933 Please note that this message will contain a full copy of the comment thread, including the initial issue submission, for this request, not just the latest update. Category: None Group: None Status: Open Resolution: None Priority: 5 Private: No Submitted By: Adam Drzewiecki (maximuser) Assigned to: Nobody/Anonymous (nobody) Summary: spherical_harmonic switches phase for odd values of m Initial Comment: I detected that spherical_harmonic function switches phase of functions with odd values of m. Help file reference towards Merzbacher 9.64 (in fact this is 9.65), but results from Maxima doesn't correspond to sample formulas in 9.68 (and http://mathworld.wolfram.com/SphericalHarmonic.html) - see Y1, +-1 and Y2, +- 1. Maxima gives formula with opposite phase (sign). this is probably due to use factor (-1)^m both in spherical_function and assoc_legendre_p (which gives proper results according to http://mathworld.wolfram.com/AssociatedLegendrePolynomial.html). Formula 9.64 in Merzbacher includes (-1)^m factor, but it is ommited in 9.59 - definition of associated Legendre polynomials. The problem is described in http://mathworld.wolfram.com/Condon-ShortleyPhase.html. I suggest omitting (-1)^m factor in definition of spherical_harmonic and/or some description in help file for spherical_harmonic. Temporary formula Y(l, m, theta, phi):=(-1)^m*spherical_harmonic(l, m, theta, phi); works fine. ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3411198&group_id=4933 ```

 [Maxima-bugs] [ maxima-Bugs-3411198 ] spherical_harmonic switches phase for odd values of m From: SourceForge.net - 2011-09-18 11:40:18 ```Bugs item #3411198, was opened at 2011-09-18 13:40 Message generated for change (Tracker Item Submitted) made by maximuser You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3411198&group_id=4933 Please note that this message will contain a full copy of the comment thread, including the initial issue submission, for this request, not just the latest update. Category: None Group: None Status: Open Resolution: None Priority: 5 Private: No Submitted By: Adam Drzewiecki (maximuser) Assigned to: Nobody/Anonymous (nobody) Summary: spherical_harmonic switches phase for odd values of m Initial Comment: I detected that spherical_harmonic function switches phase of functions with odd values of m. Help file reference towards Merzbacher 9.64 (in fact this is 9.65), but results from Maxima doesn't correspond to sample formulas in 9.68 (and http://mathworld.wolfram.com/SphericalHarmonic.html) - see Y1, +-1 and Y2, +- 1. Maxima gives formula with opposite phase (sign). this is probably due to use factor (-1)^m both in spherical_function and assoc_legendre_p (which gives proper results according to http://mathworld.wolfram.com/AssociatedLegendrePolynomial.html). Formula 9.64 in Merzbacher includes (-1)^m factor, but it is ommited in 9.59 - definition of associated Legendre polynomials. The problem is described in http://mathworld.wolfram.com/Condon-ShortleyPhase.html. I suggest omitting (-1)^m factor in definition of spherical_harmonic and/or some description in help file for spherical_harmonic. Temporary formula Y(l, m, theta, phi):=(-1)^m*spherical_harmonic(l, m, theta, phi); works fine. ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3411198&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-3411198 ] spherical_harmonic switches phase for odd values of m From: SourceForge.net - 2011-09-19 11:53:54 ```Bugs item #3411198, was opened at 2011-09-18 06:40 Message generated for change (Comment added) made by willisbl You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3411198&group_id=4933 Please note that this message will contain a full copy of the comment thread, including the initial issue submission, for this request, not just the latest update. Category: None Group: None Status: Open Resolution: None Priority: 5 Private: No Submitted By: Adam Drzewiecki (maximuser) >Assigned to: Barton Willis (willisbl) Summary: spherical_harmonic switches phase for odd values of m Initial Comment: I detected that spherical_harmonic function switches phase of functions with odd values of m. Help file reference towards Merzbacher 9.64 (in fact this is 9.65), but results from Maxima doesn't correspond to sample formulas in 9.68 (and http://mathworld.wolfram.com/SphericalHarmonic.html) - see Y1, +-1 and Y2, +- 1. Maxima gives formula with opposite phase (sign). this is probably due to use factor (-1)^m both in spherical_function and assoc_legendre_p (which gives proper results according to http://mathworld.wolfram.com/AssociatedLegendrePolynomial.html). Formula 9.64 in Merzbacher includes (-1)^m factor, but it is ommited in 9.59 - definition of associated Legendre polynomials. The problem is described in http://mathworld.wolfram.com/Condon-ShortleyPhase.html. I suggest omitting (-1)^m factor in definition of spherical_harmonic and/or some description in help file for spherical_harmonic. Temporary formula Y(l, m, theta, phi):=(-1)^m*spherical_harmonic(l, m, theta, phi); works fine. ---------------------------------------------------------------------- >Comment By: Barton Willis (willisbl) Date: 2011-09-19 06:53 Message: Thank you for the detailed analysis. I proposed using the definition in dlmf; specifically http://dlmf.nist.gov/14.30#E3. ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3411198&group_id=4933 ```

No, thanks