Oh, this is good! (I had in mind something involving differences and interpolation that I saw in Lester R. Ford's great text Differential Equations.)
Thanks, Raul! I hope you noticed Pascal's triangle lurking in my puzzles. Verb (iii0 + iii1) involved in conventional notation (1+x)^3 , and (v0+v1) , (1-x)^5 as the "generating functions". Kip Raul Miller wrote: > On Tue, Aug 18, 2009 at 5:27 PM, Kip Murray<[email protected]> wrote: >> (v0 ,: v1) 10 >> 1 6 31 76 141 226 331 456 601 766 <-- 10 from first >> sequence >> 0 _6 _32 _108 _384 _1250 _3456 _8232 _17408 _33534 <-- 10 from second >> sequence >> >> Have you seen a polynomial-fitting verb for data such as iii0 10 and iii1 10 >> ? > > (%. ^/~...@i.@#) x:1 6 31 76 141 226 331 456 601 766 > 1 _5 10 0 0 0 0 0 0 0 > 1 _5 10 p. i. 10 > 1 6 31 76 141 226 331 456 601 766 > (%. ^/~...@i.@#) x:0 _6 _32 _108 _384 _1250 _3456 _8232 _17408 _33534 > 0 0 0 _10 5 _1 0 0 0 0 > >> Did you look at (iii0 + iii1) 10 ? > > If I recall correctly, it was > 3 ^~1+i.10 > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
