Dan Bron wrote: > John Randall asked: >> Given that the xth Chebyshev polynomial evaluated at y can be written >> cos x*arccos y >> is there a way to write it using inverses? > > Yes > cheb0 =: 2 _2 */ .o. , > > If you were asking if there's a way to write this with &. (under), I > think the answer is no. Under is used when you want to transform an > input, apply a function to the transformed input, and invert the > transformation. The key here is that the inverse is applied to the output > of the function.
Thanks for the detailed and informative response, Dan. I was thinking more naively along these lines: t3=:0 _3 0 4&p. T3=:13 : 'cos 3&* arccos y' f =:3&* &. arccos Here t3 is the usual 3rd Chebyshev polynomial, T3 is its expression in trigonometric functions, and f is an equivalent expression using under. (t3,T3,f) 20 31940 31940 31940 What I can't do is make the 3 a parameter. As you indicate, it may be impossible in a verb. Perhaps if one really wanted to do this, one should use an adverb instead. Best wishes, John ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
