New extension for Associated Legendre Functions (ALFs)

Brian Gough
Tue Mar 17 11:37:00 GMT 2009

At Mon, 16 Mar 2009 15:31:37 -0600,
Patrick Alken wrote:
>   Most current implementations of associated Legendre functions
> (ALFs), including the current GSL version fail due to underflow
> above degree and order (L,M) 1900.  A 2002 paper by Holmes and
> Featherstone shows that with a very simple scaling modification
> this limit can be extended to 2700 in double precision. I have
> recently needed to compute high degree ALFs so I have implemented
> their algorithm and made a new GSL extension if others are interested.

Great work!

Incidentally, I found a copy of their paper online at

Brian Gough

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