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Re: LegendreP -- up to which order?
I did a lengthy calculation once involving Legendre and other polynomials of high order (up in the 60s) and got remarkably accurate results (IMHO, anyway). However I discovered that it made an observable difference at high enough orders whether the arguments were integers or reals. If the arguments were reals I could see observable differences between the results from two calculations that should theoretically have given identical results; but if I entered an argument of 1.001 Pi in the form 1001 Pi/1000, for example, the results of the two alternative calculations would agree exactly.