I'm pretty convinced that the general legendre polynomials are incorrect in some cases and lead to the associated legendre polynomials and spherical harmonics to be incorrect in these cases. here is the legendre polynomial as calculated on this site: https://paulmasson.github.io/sagemath-docs/functions/gen_legendre_P.html for n = 1 and m = 1:
<https://lh3.googleusercontent.com/-g55MWDsUJ2Q/W1obr3hidQI/AAAAAAAAAL0/H8RVjE7zIi4vRRQBrLqOTZgiHEX-fz0EQCLcBGAs/s1600/sagetest_2.JPG> which is what i get if i use in sagemath. but by using your definition that you state on this same website: I computed what it and the reparameterized associated legendre polynomial should be: > and this is the correct version but when i try to calculate the reparameterized associated legendre polynomial with sagemath using the general legendre polynomial function, i get <https://lh3.googleusercontent.com/-kXLSbTEWmks/W1oc0jwNR2I/AAAAAAAAAME/x62IUMhX6f05DXM4HH2JtsnHp8EViOklACLcBGAs/s1600/sagetest.JPG> if you check against outside sources like https://en.wikipedia.org/wiki/Associated_Legendre_polynomials and http://mathworld.wolfram.com/AssociatedLegendrePolynomial.html you can clearly see that whatever actual definition of the gen_legendre_P() is not what is described on the sagemath page and it is affecting spherical harmonics function. -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
