Hello,
I was wondering the difference between Sage's spherical_harmonic (as well as Maxima's spherical_harmonic) and Mathematica's SphericalHarmonicY for the same arguments.
Sage's
print(spherical_harmonic(1,1,pi/3,pi/6).n())
print(spherical_harmonic(1,-1,pi/3,pi/6).n())
gives the following results:
0.149603355150537 - 0.259120612103502*I
-0.259120612103502 + 0.149603355150537*I
Maxima's
print(maxima.spherical_harmonic(1,1,pi/3,pi/6).n())
print(maxima.spherical_harmonic(1,-1,pi/3,pi/6).n())
gives
0.259120612103502 + 0.149603355150537*I
-0.259120612103502 + 0.149603355150537*I
and Mathematica,
SphericalHarmonicY[1, 1, Pi/3, Pi/6] // N
SphericalHarmonicY[1, -1, Pi/3, Pi/6] // N
gives
-0.259121 - 0.149603*I
0.259121 - 0.149603*I
I have come across the convention difference between Maxima and Mathematica in some textbooks-- that is the (-1)^m factor, but I am not quite sure if I get it for between Sage's and Mathematica's.
So, what is the mathematical relationship between Sage's spherical_harmonic and Mathematica's SphericalHarmonicY ?
Thanks alot.
