Thanks. If that is the case, then presumably this *is* a bug in Sage Math and Func_assoc_legendre_P should distinguish the special cases for n == m when x > 1 or x < 1 when evaluating associated Legendre polynomials.
Would you be able to clarify the distinction between Ferrers functions of the first kind and associated Legendre functions for a non-expert? Wolfram Mathworld seems to suggest that they are the same: http://mathworld.wolfram.com/FerrersFunction.html On Thursday, 22 March 2018 15:23:03 UTC, Howard Cohl wrote: > > > > On Thursday, March 22, 2018 at 3:25:06 AM UTC-7, Samuel Lelievre wrote: >> >> Ralf wrote: >> > Thanks, >> > P.S. Still someone should contact DLMF with the right arguments. >> >> I just emailed them with cc to sage-devel. >> > > There's nothing wrong with the formula. The Legendre function in the DLMF > is for arguments greater than 1, and is not valid for arguments less than > one. For arguments less than one the correct formula is > > P_m^m(x)=(-1)^m (2m)!/(2^m m!) (1-x^2)^(m/2). > > Both of these are easy to derive using the well-known formulae for > P_\nu^{-\nu} and {\sf P}_\nu^{-\nu} and the connection formulas which > relate P_{\nu}^{-m} to P_{\nu}^m, and for Ferrers functions. See > http://dlmf.nist.gov/14.5.iv <https://dlmf.nist.gov/14.5.iv> and > https://dlmf.nist.gov/14.9. > Where P is the associated Legendre function of the first kind, and {\sf P} > is the Ferrers function of the first kind. > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
