Recent changes to 45: Make orthopoly_recur(legendre_p, ...) indices consistenthttps://sourceforge.net/p/maxima/patches/45/Recent changes to 45: Make orthopoly_recur(legendre_p, ...) indices consistentenWed, 01 Aug 2012 21:14:18 -0000Make orthopoly_recur(legendre_p, ...) indices consistenthttps://sourceforge.net/p/maxima/patches/45/The recurrence relation given by orthopoly\_recur\(\) for legendre\_\{p,q\}\(\) is inconsistent with relations for other polynomials in that it gives the Legendre polynomial of degree \(n\) in terms of polynomials of degree \(n-1\) and \(n-2\) instead of giving the \(n+1\) polynomial in terms of \(n\) and \(n-1\) like the others. This patch makes it consistent with the other results \(such as assoc\_legendre\_\{p,q\}\) and with A&S p782.
This patch also corrects two recurrence relations \(ultraspherical and hermite\) in the comments. orthopoly\_recur\(\) gives the same relations as A&S, but there were sign errors in the comments.
To avoid possibly garbled text, I'll also attach a file showing the previous result for legendre\_p\(n,x\), the result for assoc\_legendre\_p\(n,0,x\) and the new result for legendre\_p\(n,x\), showing that the latter two are in the same form. \(I guess I can upload other files after I initially submit this\).
Thanks,
Kris KatterjohnKris KatterjohnWed, 01 Aug 2012 21:14:18 -0000https://sourceforge.net6fa9de0d83a81aa68910ec5cbfe108aa0dbc1328