4:42 AM
@uhoh Great, no problem! Leaving a few more comments here since after digging into this is proving that there is more complexity into it than I originally thought, but seems like (almost) all of the pieces are coming together slowly
There seems to be multiple ways to calculate the values of associated Legendre functions and their derivatives based on recursive relationships, the exact expressions change depending on the chosen normalization and, when using spherical coordinates, chosen meaning for the angles (i.e., most depending on if longitude/colongitude and latitude/colatitude are chosen)
The implementation I'm using for it is the recursive relationships described in page A-2.1 (page 107 of the PDF file) here repository.tudelft.nl/islandora/object/…

4:57 AM

With a small difference, which is that I am using latitude instead of the co-latitude (polar angle, the theta in the document) used in that document, so all sines are swapped to cosines and vice versa. Also there's a small print mistake in the second equation for the diagonal recursion. That is in fact the equation for the first order derivative of the Legendre functions, i.e., all the terms in that equation are missing a ' symbol

5:15 AM
I have tried to dig into the sci-py code used by sph_harm . It seems it calls the lpmv function, which unluckily is a wrapper for the LPMV routine here github.com/scipy/scipy/blob/main/scipy/special/specfun/… , which is written in FORTRAN77... I tried to decipher it for a while but unluckily I'm at a complete loss in FORTRAN. So hard to say exactly what recursive relationship they use to calculate the Legendre polynomials (which in turn would allow to verify normalization)
Maybe someone with knowledge in FORTRAN could help? But alternatively, I guess it would be possible to output a matrix of the associated Legendre polynomial functions by calling sci-pi's lpmv, for let's say degree and order 100, and a few values (maybe 0, pi/4 and pi/2?), and compare it to the values I get to see if they match... I'll try to see if I can do this at some point!

7 hours later…
11:57 AM
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Say, I want to edit a question by an OP to show how to improve it. For various reasons, I do not want to reveal who is making this suggestion. Is it possible?

3 hours later…
2:54 PM
@XKCD Very funny and also very wise question. I think here could psychology help science a lot.

6 hours later…
8:56 PM
0

The CNN video Experts on what North Korea's series of missile tests may mean summarizes several tests of different "flying objects" including (apparently) two hypersonic missiles (BBC: North Korea successfully tested hypersonic missile, says report). From the video (my transcription): North Kore...

9:34 PM
@uhoh Interesting, if they have figured out a loop hole on that one... Isreal is the only country that launches against the rotation of the Earth. (Launches westwards). Imagine launching to the East, kinda looks like an ICBM attack so I get why they try not to aggravate folk.
But they lose payload to orbit due to that.
Starlink launch tonight at 7PM EST. Polar orbit from KSC, heading southeast... (Better weather for landing than north east).
Core B1060 on its 10th flight! (4th core to hit 10 flights if it succeeds!) 11, 10,10,9 are the current fleet leaders. (This is the 9, soon to be 10).
ASOG for the catch. ANd more launches still on tap in Jan!!! CSG which is an RTLS I think, Jan 28th! And maybe another snuck in before... Schedule is hard to get nauiled down.

9:52 PM
they're launching from KFC?